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Physics 212
Sample Question Bank II
If the charge on a given capacitor is doubled, then
(A)
the capacitance doubles.
(B)
the potential difference across the capacitor doubles.
(C)
the permeability of free space doubles.
(D)
the energy stored in the capacitor doubles.
(E)
all of the above.
Consider the two air capacitors arranged in the circuit as shown.
The plates of capacitor C2 have twice the area but the same
separation as the plates of C1. We can say that
(A)
C2 has twice the capacitance as C1 .
(B)
C2 carries twice the charge as C1 .
(C)
C2 stores twice the energy as C 1 .
(D)
C2 has the same voltage as C1 .
(E)
All of the above
2011
C2
C1
d
A
d
2A
If the potential difference (i.e. voltage) on a given capacitor is doubled, then
(A) the capacitance is halved.
(B) the charge on the capacitor doubles.
(C) the permeability of free space doubles.
(D) the energy stored in the capacitor doubles.
(E) all of the above.
The dielectric constant for a material is
(A) the factor by which the capacitance decreases when the material is inserted between the plates of a
parallel plate capacitor.
(B) the factor by which the magnitude of the electric field decreases when the material is inserted
between the plates of a parallel plate capacitor.
(C) the factor by which the potential increases when the material is inserted between the plates of a
parallel plate capacitor.
(D) the minimum electric field the material can withstand before dielectric breakdown.
(E) (A) through (C) the above.
The dielectric constant for a material is
(A) the factor by which the capacitance increases when the material is inserted between the plates of a
parallel plate capacitor.
(B) the factor by which the magnitude of the electric field decreases when the material is inserted
between the plates of a parallel plate capacitor.
(C) the factor by which the potential decreases when the material is inserted between the plates of a
parallel plate capacitor.
(D) the maximum electric field the material can withstand before dielectric breakdown.
(E) (A) through (C) the above.
1
Physics 212
Sample Question Bank II
2011
The dielectric strength for a material is
(A) the factor by which the capacitance increases when the material is inserted between the plates of a
parallel plate capacitor.
(B) the factor by which the magnitude of the electric field decreases when the material is inserted
between the plates of a parallel plate capacitor.
(C) the factor by which the potential decreases when the material is inserted between the plates of a
parallel plate capacitor.
(D) the maximum electric field the material can withstand before dielectric breakdown.
(E) (A) through (C) the above.
A parallel plate capacitor is charged by being connected to a battery and is then disconnected from the battery.
The separation between the plates is then doubled. The electric field strength between the plates
(A)
doubles.
(B)
stays the same.
(C)
is reduced by a factor of one-half.
(D)
is reduced by a factor of one-quarter.
(E)
becomes zero as soon as the capacitor is disconnected from the battery.
A parallel plate capacitor is charged by being connected to a battery. It remains connected to the battery as the
separation between the plates is then doubled. The charge on the capacitor
(A)
doubles.
(B)
stays the same.
(C)
is reduced by a factor of one-half.
(D)
is reduced by a factor of one-quarter.
(E)
becomes zero as soon as the capacitor is disconnected from the battery.
A parallel plate capacitor is charged by being connected to a battery, and while remaining connected to the
battery a dielectric (K = 3) insulating material is placed between the plates of the capacitor. As a result of
inserting the dielectric, the charge on the capacitor
(A)
increases.
(B)
decreases.
(C)
stays the same.
(D)
reverses sign.
(E)
becomes zero as soon as the dielectric is inserted.
The effective capacitance of two capacitors connected in series is
(A)
always less than the individual capacitance of either of the two capacitors .
(B)
always greater than the individual capacitance of either of the two capacitors .
(C)
always between than the individual capacitances of the two capacitors .
(D)
none of the above always holds.
The effective capacitance of two capacitors connected in parallel is
(A)
always less than the individual capacitance of either of the two capacitors .
(B)
always greater than the individual capacitance of either of the two capacitors .
(C)
always between than the individual capacitances of the two capacitors .
(D)
none of the above always holds.
2
Physics 212
Sample Question Bank II
2011
Consider three air filled parallel plate capacitors. Capacitor B has twice the area for each plate and the same
plate separation, compared to A. Capacitor C has twice the plate separation and the same area for each
plate, compared to A. When ranked by their capacitance from greatest to smallest, then
(A)
CA > CB >CC.
(B)
CA > CB = CC.
(C)
CB > CA > CC.
(D)
CB = CC > CA.
(E)
CA = CB = CC.
A solid slab of conductor is placed between the plates of a parallel plate capacitor (without
touching either plate) as shown. The slab has the same area as the capacitor plates.
The effective capacitance of the device
(A)
increases.
(B)
decreases.
(C)
stays the same.
(D)
changes unpredictably.
The principles used to derive the expressions for equivalent capacitances of series and parallel combinations of
capacitors were
(A)
conservation of energy and conservation of momentum.
(B)
conservation of energy and conservation of charge.
(C)
conservation of charge and conservation of momentum.
(D)
symmetry and conservation of energy.
(E)
no principles are required as the necessary equations can be found in the chapter summary.
The principles used to derive the expressions for equivalent resistance of series and parallel combinations of
resistors were
(A)
conservation of energy and conservation of momentum.
(B)
conservation of energy and conservation of charge.
(C)
conservation of charge and conservation of momentum.
(D)
symmetry and conservation of energy.
(E)
no principles are required as the necessary equations can be found in the chapter summary.
Electric Current
(A)
is measured in units of Amperes.
(B)
is synonymous with drift velocity.
(C)
does not diminish as it progresses through a circuit.
(D)
all of the above.
(E)
none of the above.
Two wires of different diameters but made of the same material are joined end to end. When the current flows in
the wire, electrons move from the wire of larger diameter into the wire with smaller diameter. As the
electrons pass through this junction, their drift speed
(A)
increases.
(B)
remains fixed.
(C)
decreases.
(D)
goes to zero.
(E)
may change, but more information is required to determine the change.
3
Physics 212
Sample Question Bank II
2011
Two wire segments made of the same material have the same length but different diameter. They are connected
in series to a battery. The quantity that is the same for the two wires is:
(A)
the potential difference across the length of each segment.
(B)
the current in each segment.
(C)
the current density in each segment.
(D)
the electric field in each segment.
(E)
the electron drift velocity in each segment.
Kirchoff's loop rule is essentially a statement of
(A)
conservation of charge.
(B)
conservation of momentum
(C)
conservation of energy
(D)
conservation of angular momentum
(E) none of the above.
Kirchoff's junction rule (or point rule) is essentially a statement of
(A)
conservation of charge.
(B)
conservation of momentum
(C)
conservation of energy
(D)
conservation of angular momentum
(E)
none of the above.
Since the resistance of a human body can be as low as 1000Ω and a current of .1A can be fatal, a safety
mechanism can be designed into a high-voltage power supply by
(A)
having a low internal resistance which will maximize the current delivered.
(B)
having a 1000Ω to maximize the power delivered.
(C)
having a high internal resistance to limit the maximum current which could be delivered.
(D)
having a low EMF to limit the maximum current which could be delivered.
A physics professor with a body resistance of 10kΩ accidentally grips the terminals of a 10kV power supply
which has an internal resistance of 10kΩ. If a potentially lethal shock occurs when the current exceeds
100mA, then the professor
(A)
is in need of a call to 911, since the current is well in excess of 100 mA.
(B)
may be in need of a call to 911, since the current is about 100 mA.
(C)
is swearing loudly but is largely unharmed because the current was well below 100mA.
(D)
is vaporized since 10kV exceeds his dielectric strength.
(E)
trick question, my physics professor would never do such thing (do not pick
this answer, it is for humor purposes only!).
A physics professor with a body resistance of 10kΩ accidentally grips the terminals of a 10kV power supply
which has an internal resistance of 10MΩ. If a potentially lethal shock occurs when the current exceeds
100mA, then the professor
(A)
is in need of a call to 911, since the current is well in excess of 100 mA.
(B)
may be in need of a call to 911, since the current is about 100 mA.
(C)
is swearing loudly but is largley unharmed because the current was well below
100 mA.
(D)
is vaporized since 10kV exceeds his dielectric strength.
(E)
trick question, my physics professor would never do such thing (do not pick
this answer, it is for humor purposes only!).
4
Physics 212
Sample Question Bank II
2011
The potential difference between the terminals of a real battery (emfE, internal resistance r) can be exactly the
same as the emf in magnitude and polarity if
(A)
the battery is shorted out (zero load resistance).
(B)
there is an infinite load resistance (open circuit).
(C)
the battery is being charged by an external source.
(D)
an external source helps drive a large current through the battery in the direction it would
naturally discharge.
(E)
never.
The potential difference between the terminals of a real battery (emfE internal resistance r) can have the opposite
polarity (direction) of the emf if
(A)
the battery is shorted out (zero load resistance).
(B)
there is an infinite load resistance.
(C)
the battery is being charged by an external source.
(D)
an external source helps drive a large current through the battery in the direction it would
naturally discharge.
(E)
never.
The current-voltage characteristics at right indicate a
device whose resistance is
(A)
increasing with increasing current.
(B)
remaining constant.
(C)
decreasing with increasing current.
(D)
changing uncontrollable with increasing
current.
(E) none of the above.
The current-voltage characteristics at right indicate a
device whose resistance is
(A)
increasing with increasing current.
(B)
remaining constant.
(C)
decreasing with increasing current.
(D)
changing uncontrollable with increasing
current.
(E) none of the above.
I
V
I
V
5
Physics 212
Sample Question Bank II
2011
The current versus voltage graph which corresponds to a device whose resistance increases with increasing
voltage:
(A)
(C)
(B)
(D)
(E) None of the above
A real battery delivers maximumpower when
(A)
the load resistance is zero.
(B)
the load resistance matches the internal resistance of the battery.
(C)
the load resistance is infinite.
(D)
the power is the same regardless of the load resistance.
(E)
none of the above.
A real battery delivers maximumcurrent when
(A)
the load resistance is zero.
(B)
the load resistance matches the internal resistance of the battery.
(C)
the load resistance is infinite.
(D)
the current is the same regardless of the load resistance.
(E)
none of the above.
A real battery has a maximum terminalvoltage when
(A)
the load resistance is zero.
(B)
the load resistance matches the internal resistance of the battery.
(C)
the load resistance is infinite.
(D)
the terminal voltage is the same regardless of the load resistance.
(E)
none of the above.
Two wires of different metallic conductors with the same diameters are joined end to end. As the current from
the wire with lower resistivity into the wire with higher resistivity,
(A)
the current decreases.
(B)
the current density decreases.
(C)
the electric field decreases.
(D)
the electric field increases.
(E)
the electrons stop moving.
6
Physics 212
Sample Question Bank II
2011
The effective resistance of two resistors connected in parallel is
(A)
always less than the individual resistance of either of the two resistors .
(B)
always greater than the individual resistance of either of the two resistors .
(C)
always between than the individual resistance of the two resistors .
(D)
always less than the individual resistance of either of the two resistors .
(E)
none of the above always holds.
The effective resistance of two resistors connected in series is
(A)
always less than the individual resistance of either of the two resistors .
(B)
always greater than the individual resistance of either of the two resistors .
(C)
always between than the individual resistance of the two resistors .
(D)
always less than the individual resistance of either of the two resistors .
(E)
none of the above always holds.
Two identical light bulbs are connected in series to an ideal battery as shown. In
this configuration
(A) Bulb A will glow brighter than Bulb B.
(B) Bulb B will glow brighter than Bulb A.
(C) Only Bulb A will glow.
(D) Only Bulb B will glow.
(E) both bulbs will glow equally bright.
Bulb A
Bulb B
Two light bulbs are connected in series to an ideal battery as shown. The bulbs
have different resistances. The thing that will be the same for both bulbs
will be
(A) the voltage drop across the bulbs.
(B) the current through the bulbs.
(C) the power dissipated in the bulbs.
(D) all of the above.
(E) none of the above.
Two light bulbs are connected in parallel to an ideal battery as shown. In this
configuration, the bulb that glows brighter (i.e. dissipates the greatest
power) will be
(A) the bulb with the greatest resistance.
(B) the bulb with the smallest resistance.
(C) both bulbs will dissipate the same power.
(D) the top bulb.
(E) the bottom bulb.
Three light bulbs are connected to an ideal battery as shown. In this configuration, The ranking of the bulbs,
from brightest to dimmest will be
(A) A=B=C.
B
(B) B=C>A.
A
(C) A>B=C.
(D) A>B>C.
(E) B>A>C.
C
7
Physics 212
Sample Question Bank II
2011
Resistors of resistance R or 2R (twice the resistance of the first kind) are connected in the following circuits.
The EMF of the battery is the same for all circuits. Rank the circuits by current drawn from the battery,
from greatest to least.
I2
I1
(A) I 1 I 2 I 3I 4 .
(B) I 1= I 4 I 2=I 3 .
(C) I 4I 1= I 2=I 3 .
2R
R
(D) I 1 I 2= I 3I 4 .
(E) I 4I 2=I 3 I 1 .
I4
I3
R
R
2R
2R
The principles used to to analyze electrical circuits in the last three chapters were
(A)
conservation of energy and conservation of momentum.
(B)
conservation of charge and conservation of momentum.
(C)
symmetry and conservation of energy.
(D)
conservation of energy and conservation of charge.
(E)
all of the above.
Ideal voltmeters and ideal ammeters have resistances which are
(A)
both zero.
(B)
both infinite.
(C)
zero and infinite, respectively.
(D)
infinite and zero, respectively.
(E)
none of the above.
An ammeter is a measurement apparatus which
(A) is used to measure the voltage across a device by placing the meter in series with the device.
it has infinite resistance.
(B) is used to measure the current through a device by placing the meter in parallel with the
Ideally it has infinite resistance.
(C) is used to measure the current through a device by placing the meter in series with the device.
it has zero resistance.
(D) is used to measure the voltage across a device by placing the meter in parallel with the
Ideally it has infinite resistance.
(E) is used to measure the resistance of a device by placing the meter in parallel with the device.
it has matching resistance.
Ideally
device.
Ideally
device.
Ideally
8
Physics 212
Sample Question Bank II
2011
An voltmeter is a measurement apparatus which
(A) is used to measure the voltage across a device by placing the meter in series with the device.
it has infinite resistance.
(B) is used to measure the current through a device by placing the meter in parallel with the
Ideally it has infinite resistance.
(C) is used to measure the current through a device by placing the meter in series with the device.
it has zero resistance.
(D) is used to measure the voltage across a device by placing the meter in parallel with the
Ideally it has infinite resistance.
(E) is used to measure the resistance of a device by placing the meter in parallel with the device.
it has matching resistance.
Ideally
device.
Ideally
device.
Ideally
The current versus voltage graph which best represents a device which obeys Ohm's Law:
(A)
(B)
(C)
(D)
(E) none of the above.
9
Physics 212
Sample Question Bank II
2011
A series RC circuit with an initially uncharged
capacitor is connected as shown. The switch is
closed at t=0. Which graph below best describes
current through the resistor as a function of
time?
(A)
(B)
i
i
10
14
t
(C)
(D)
i
i
t
t
(E) none of the above.
A series RC circuit with an initially charged
capacitor is connected as shown. The switch is
closed at t=0. Which graph below best describes
the current as a function of time?
(A)
(B)
i
10
14
t
(C)
(D)
i
i
t
t
(E) none of the above.
10
Physics 212
Sample Question Bank II
2011
READ CAREFULLY: A series RC circuit with an initially uncharged capacitor is connected to a switch as
shown. The switch is closed at t=0. Which graph below best describes the voltage drop across the capacitor?
(A)
i
(C)
i
t
t
(B)
i
i
(D)
10
14
t
(E) none of the above.
As a capacitor is being charged in a series RC circuit, current flowing into the capacitor will:
(A) increase.
(B) decrease.
(C) remain the same.
(D) oscillate.
(E) vacillate.
You could increase the time constant of an RC circuit by
(A)
adding a resistor in parallel with the circuit resistance.
(B)
adding a capacitor in parallel with the circuit capacitance.
(C)
increasing the voltage of the charging battery.
(D)
exchanging the position of the resistor and capacitor in the circuit.
A capacitor and a resistor are connected in series across the terminals of a battery. If the capacitance is
increased, then
(A)
the final charge on the capacitor is increased.
(B)
the final charge on the capacitor is decreased.
(C)
the final charge on the capacitor is the same, but the capacitor charges more slowly.
(D)
both (A) and (C) above.
(E)
both (B) and (C) above.
A capacitor and a resistor are connected in series across the terminals of a batty. If the resistance is increased,
then
(A)
the final charge on the capacitor is increased.
(B)
the final charge on the capacitor is decreased.
(C)
the final charge on the capacitor is the same, but the capacitor charges more slowly.
(D)
the final charge on the capacitor is the same, but the capacitor charges more quickly.
(E)
none of the above.
11
Physics 212
Sample Question Bank II
2011
A +4 µF capacitor is connected in series with a 2.5 kΩ resistor. The time constant of this combination is
(A)
1. x 10+2 s.
(B)
1. x 10-5 s.
(C)
1. x 10-2 s.
(D)
1. x 10+1 s.
(E)
none of the above.
A capacitor and a resistor are connected in series across the terminals of a batty. If the resistance is increased,
then
(A)
the final charge on the capacitor is increased.
(B)
the final charge on the capacitor is decreased.
(C)
the final charge on the capacitor is the same, but the capacitor charges more slowly.
(D)
the final charge on the capacitor is the same, but the capacitor charges more quickly.
(E)
none of the above.
12
Physics 212
Sample Question Bank II
Part II Problems
(15 points each).
Show all work. No work = no credit!
2011
For the diagram shown below
a) Calculate the equivalent capacitance of the capacitor
network, and the energy stored in the
equivalent capacitance.
b) Calculate the charge on each capacitor, the potential
difference across each capacitor and the
energy stored in each capacitor.
C1=3µF
C2=4µF
C3=3µF
48V
C4=6µF
____________________________________________________________
For the diagram shown below
a)
Calculate the equivalent capacitance of the
capacitor network, and the energy stored in the
equivalent capacitance.
b) Calculate the charge on each capacitor, the
potential difference across each capacitor and
the energy stored in each capacitor
C 2=6µ F
C 1=6µ F
C 3=2µ F
96 V
C 4=4µ F
____________________________________________________________
A capacitor with plates of area A and separation d is completely filled
with a “leaky” dielectric with dielectric constantK and resistivity ρ.
When the capacitor has a charge Q, there is a leakage current I.
(A) Determine the resistance of the dielectric slab in terms of the
parameters listed above.
(B) Determine the capacitance of the capacitor in terms of the
parameters listed above.
(C) Determine the voltage across the capacitor in terms of the
parameters listed above.
(D) The voltage across the capacitor drives the leakeage current
through the dielectric. Express the current in terms of the
parameters listed above.
(E) What is the RC time constant of this combination of resistor and
capacitor? (expressed in terms of the parameters listed above)
13
Physics 212
Sample Question Bank II
An air parallel plate capacitor is to be made using plates that are each 0.025 m2
in area. Their initial separation is 0.050 cm. They are charged with a 12.0 V
source which is then disconnected.
2011
a) What is the original capacitance of the capacitor?
b) What is the charge on the capacitor?
c) What is the initial energy stored in the capacitor?
The separation between the plates is increased to 0.100cm.
c) What is the new capacitance of the capacitor?
d) What is the new energy stored in the capacitor?
e) How much mechanical work went into increasing the separation between
the plates?
____________________________________________________________
An air parallel plate capacitor is to be made using plates that are each 0.0125 m2 in area. The
separation between the plates is 0.0250 cm. The capacitor is charged with a 10.0 V
source which is then disconnected.
a) What is the original capacitance of the capacitor?
b) What is the charge on the capacitor?
c) What is the initial energy stored in the capacitor?
A third metal plate of thickness .0150 cm and 0,0125 m2 in area is inserted between the plates,
exactly centered in the original .0250 cm gap, creating a new capacitance that is essentially two
capacitors in series.
d) What is the new capacitance of the object?
e) What is the new energy stored in the capacitor (that still has the charge from part b)?
f) How much mechanical work would be required to extract that plate from the charged capacitor?
____________________________________________________________
A parallel plate capacitor is to be made using a material whose who dielectric constant is 4.7 and whose dielectric
strength is 1x107 V/m. The capacitor is to have a capacitance of 500 nF, and must withstand a potential
difference 1000 V with suffering dielectric breakdown.
a) What is the minimum separation between the plates of the capacitor?
b) Using this minimum separation, determine the area of each plate for the design capacitance.
If this capacitor has 500 V applied, determine
c) the charge on the capacitor,
d) the electric field between the plates, and
e) the energy stored in the capacitor.
____________________________________________________________
14
Physics 212
Sample Question Bank II
2011
A parallel-plate capacitor is to be constructed using a dielectric material which has a dielectric constant of 3.4
and a dielectric strength of 2.00x107 V/m. The capacitor is to have a capacitance of 2nF and must
withstand a potential differences up to 6000V.
(A) Determine the minimum separation (D) between the plates by taking the strength (E) of the uniform electric
field between the plates to be equal to the dielectric strength of the material when the applied potential
(Vab) is equal to the design maximum (6000V).
(B) Determine the area of each plate if the capacitor has the design capacitance and a plate separation as
determined in part (A). (Remember to account for the dielectric constant in your calculation).
____________________________________________________________
You need a capacitor of capacitance 40µF that can withstand a voltage of 1000V. You have at
your disposal a large bin of identical capacitors of capacitance 40µF that can withstand a
voltage of 500V. Devise a network of the available capacitors that has the desired
capacitance such that the voltage on each physical capacitor does not exceed 500 V when
1000V is applied to the network. Be sure to draw the circuit diagram of your network.
What is the charge on and voltage across each capacitor when your network is attached to a
1000V source?
A
An air parallel plate capacitor is to be made using plates of areaA. Their initial separation is given
as x. The capacitor is charged with a charge Q and then disconnected from its charging battery.
a) What is the capacitance of the capacitor in terms of the parameters given?
b) What is the energy stored in this capacitor in terms of the parameters given?
c) From mechanics we learned that the relationship between the force on an object and its
x
potential energy was
dU  x 
.
F  x=
dx
Use this relation to find an expression for the force between the plates of a charged parallel plate capacitor in
terms of the parameters given.
____________________________________________________________
Suppose a capacitor has plates each of area .02 m2 separated by a distance of 4.00 mm, which is charged by a
10 V battery.
d) what is the capacitance of this capacitor?
e)what is the charge on this capacitor?
f) using your results (including your answer to part c) determine the force of attraction between the plates
of this capacitor.
____________________________________________________________
A resistor is made of a cylinder of graphite 2 cm long and .2 cm in diameter. At 20°C graphite has a resistivity of
3.5E-5 Ω·m and a temperature coefficient of resistivity of -.0005 (°C)-1.
(A) What is the resistance of the resistor at 20°C?
(B) What would be the resistance at 250°C?
(C) At what temperature would the resistance be 0.25% higher than at 20°C?
____________________________________________________________
15
Physics 212
Sample Question Bank II
2011
A resistor is made from an unknown material 2.50 cm long and .5 cm in radius. At 20°C the resistor has a
resistance of 204 kΩ and at 25°C the resistor has a resistance of 127 kΩ .
(A) What is the resistivity of the material at 20°C?
(B) What is the temperature coefficient of resistivity of the material?
(C) What would the resistance of this resistor be at 18°C?
____________________________________________________________
For the diagram shown at right
a) Calculate the equivalent resistance of the resistor
network, and the power dissipated in the
equivalent resistance.
b) Calculate the current through each resistor, the
power dissipated in each resistor, and the
potential difference across each resistor.
R1 = 8Ω
R 3 = 8Ω
R 2 = 6Ω
48V
R 4 = 4Ω
____________________________________________________________
For the diagram at right, determine
six currents indicated. Clearly indicates the loops and junctions
you are using for your application of Kirchoff’s rules on the
diagram. Clearly write the loop and junction equations you
generate. Use your calculator to solve these simultaneous
equations. Hint: to find the 6 unknown currents will require 6
equations. In this case, 3 loops and 3 junctions will likely work.
7V
I6
1Ω
Bonus (3 points) what is the effective resistance of the network
(look at the net current drawn by the network and the battery’s
voltage). (must be correct value to get any points)
Warning: there are no serial or parallel combinations in this
problem.
I1
I2
2Ω
1Ω
2Ω
I3
I4
1Ω
I5
____________________________________________________________
16
Physics 212
Sample Question Bank II
For the diagram, determine the five currents
indicated. Clearly indicates the loops and
junctions you are using for your application of
Kirchoff’s rules on the diagram. Clearly write
the loop and junction equations you generate.
Use your calculator to solve these
I2
simultaneous equations. Hint: to find the 5
unknown currents will require 5 equations.
Each current must appear in at least one
E3=24V
junction rule, and each branch must appear in
I
3
at least one loop rule. 2 junction rules and 3
branch rules will most likely work.
2011
E1=60V
R1 = 2Ω
I1
E4=6V
R2 = 18Ω
I4
R3 = 3Ω
I5
R4 = 18Ω
E5=8V
R1 = 4Ω
Warning: there are no serial or parallel
combinations of resistors in this problem.
You are given a 4 Ω resistor, a 12 Ω resistor and an 48 V battery, and are to construct a circuit with just these
elements which dissipates the maximum amount of power possible with these elements.
(A) What is the maximum power (in W) that can be dissipated in resistors? Show how you come up with this
numerical result, and why it dissipates the maximum total power.
(B) Draw a circuit diagram showing the configuration for the circuit you have chosen. How did you
determine that this configuration dissipates more power than any other?
You need a resistance of 10.0Ω that can dissipate 10.0W without failing (releasing smoke) when connected to
10.0V. You have at your disposal a large bin of identical 10.0Ω resistors that can dissipate 5.00W
without failing (releasing smoke). Devise a network of the available resistors that has the desired
resistance such that the power dissipated by each resistor does not exceed 5.00W when the network is
connected to a 10.0V source. What is current through, voltage across and power dissipated in each
physical resistor in your network? Be sure to draw the circuit diagram of your network.
17
Physics 212
Sample Question Bank II
For the diagram at right, determine
six currents indicated. Clearly indicates the loops and
junctions you are using for your application of
Kirchoff’s rules on the diagram. Clearly write the loop
and junction equations you generate. Use your
calculator to solve these simultaneous equations. Hint:
to find the 4 unknown currents will require 4
equations. In this case, 3 loops and 1 junction will
likely work.
2011
E1=100
R1 = 4Ω
I1
E2=80
R2 = 5Ω
I2
E3=20
Warning: there are no serial or parallel combinations of
resistors in this problem.
I3
R3 = 20Ω
I4
R1 = 4Ω
____________________________________________________________
A real battery has an EMF of E=15V and an internal resistance of r=5Ω .
load resistance R is placed across the terminals of the battery.
The current in the circuit is 1A.
I
A) Find the load resistance.
B) Determine the power delivered to the load resistance.
C) Determine the power dissipated in the internal resistance.
D) Determine the total power delivered by the EMF.
E
r
A
a
b
R
The battery is now disconnected from the load, and is charged by a 1 A
charging
I
r
E
current.
E) Determine the power delivered to the EMF.
a
b
F) Determine the power dissipated in the internal resistance.
G) Determine the total power delivered by the 1A charging current.
H) Calculate the efficiency of the battery as a storage device by taking the ratio of the power delivered (answer
B) to the power used in storage (answer G), x100%.
___________________________________________
In the figure shown at right, use Kirchoff’s laws to determine
(A) the unknown current I3 ,
(B) the unknown emf E, and the
(C) the unknown resistance r.
60V
r
I1=2A
I2=3A
R2=5Ω
I3
R3=10Ω
18