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UNIT – II, CURRET ELECTRICITY
Important Formulae
1Electric current =
or I = =
2. In case of an electron revolving in a circle of radius r with speed v, period of revolution is T =
Frequency of revolution, v = =
, Current, I = ev =
3. Ohm’s law, R = or V = IR
4. Current in terms of drift velocity ( ) is I = enA
5. Resistance of a uniform conductor, R =
=
6. Resistivity or specific resistance, =
=
7. Conductance =
8. Conductivity =
or σ = =
9. Current density =
or j = = en
10. Relation between current density and electric field,
j = σ E or E = j
11. Mobility µ =
12. Temperature coefficient of resistance, α =
13. The equivalent resistance
14. The equivalent resistance
of a number of resistances connected in series is given by
=
+
+
+ …..
of a number of resistances connected in parallel is given by
=
15. EMF of a cell, E =
16. For a cell of internal resistance r, the emf is E = V + Ir = I (R + r)
17. Terminal p.d of a cell, V = IR =
18. Terminal p.d. when a current is being drawn from the cell, V = E – Ir
19. Terminal p.d. when the cell is being charged, V = E + Ir
20. Internal resistance of a cell, r = R [ ]
21. For n cell in series, I =
22. For n cells in parallel, I =
23. Heat produced by electric current, H =
Rt joule =
cal
24. Electric power, P = = VI = R =
25. Electric energy, W = Pt = VIt = Rt
26. Potential gradient of the potentiometer wire,k =
27. For comparing e.m.f.s of two cells,
=
28. For measuring internal resistance of a cell,r =
29. For a balanced Wheatstone bridge, = ,
xR
If X is the unknown resistance
= or X =
30. In a slide wire bridge, if balance point is obtained at l cm from the zero end, then = =
CONCEPT MAP
Important derivation type and theoretical type of Questions
Very Short Answer Type Questions
1. Write the principle on which a meter bridge works?
2. Name the charge carriers in case of an electrolyte, an ionized gas?
3. Define current density. State whether it is a scalar or vector?
4. What happens to the drift velocity with rise of temperature?
5. Under what condition one can draw maximum current from a cell?
6. Define mobility? Write its S I unit.
7. Does the resistance change on bending or reorienting the wire?
Short Answer Type Questions-II[2 or 3 marks each]
1. State the principle of potentiometer. Draw a circuit diagram used to compare the emfs of two primary
cells . Write the formula used. How can the sensitivity of a potentiometer be increased.
2. Define the terms resistivity and conductivity and state their S.I. units. Draw a graph showing the
variation of resistivity with temperature for a typical semiconductor.
3. Define the temperature coefficient of resistivity. Write its S.I. unit. Plot a graph showing the variation
of resistivity of nichrome / copper with temperature.
4. Are the paths of electrons straight lines between successive collisions in the (i) absence of electric field
(ii) presence of electric field?
Establish a relation between drift velocity and current. Hence obtain the relation between current
density and drift velocity.
5. How does the resistivity of
(i) a conductor and (ii) a semiconductor vary with
temperature?
Give reasons.
6. Why are the connections between resistors in a meter bridge made of thick copper strips? What
happens if the galvanometer and cell are interchanged at the balance point of the bridge? Would the
galvanometer show any current?
7. Define the term resistivity and write its SI unit. Derive the expression for the resistivity of a conductor
in terms of number density of free electrons and relaxation time.
8. What is meant by drift velocity of free e’ s. Derive its expression.
9. What is meant by drift velocity of free e’ s. Derive ohm’s law on the basis of the theory of electron
drift.
10. Draw Circuit diagram for a meter bridge to determine the unknown resistance of a resistor. Obtain the
balance condition for a meter bridge. Find the shift in the balance point for a meter bridge when two
resistors in its two gaps, are interchanged.
11. With the help of a circuit diagram, explain how a potentiometer can be used to measure the internal
resistance of a primary cell.
Important numerical type of Questions
12. A pd of 30V is applied across a colour coded carbon resistor with rings of blue, black and yellow
colours. What is the current to the resistor?
13. Nichrome and Cu wires of the same length and same diameter are connected in series in an electric
circuit. In which wire will the heat be produced at a higher rate?
14. Two bulbs are marked 220V-100W and 220V-50W. They are connected in series to 220V mains. Find
the ratio of heat generated in them
15. In a potentiometer circuit, a battery of negligible internal resistance is set up as shown to develop a
constant potential gradient along the wire AB. Two cells of emfsƐ 1 and Ɛ 2 are connected in series as
shown in the combination (1) and (2). The balance points are obtained respectively at 400cm and
240cm from the point A. Find (i) Ɛ 1/ Ɛ 2 and (ii) balancing length for the cell Ɛ 1 only.
16 .In the potentiometer circuit shown, the balance point is at X.
State with reason where the balance point will be shifted when
(i)Resistance R is increased, keeping all parameters unchanged.
(ii)Resistance S is increased keeping R constant.
(iii)Cell P is replaced by another cell whose emf is lower
than that of that cell Q.
17.Find the value of the unknown resistance X and the current drawn by the circuit from the battery
if no current flows through the galvanometer. Assume the resistance per unit length of the wire is
0.01Ωcm-1 .
18.Figure shows two circuits in each having a galvanometer and a battery of 3 V. When the
galvanometers in each arrangement do not show any deflection, obtain the ratio R1 : R2.
R1
4
12
6
G
60
3.0V
R2
6
8
9
3.0V
1.20
G
19. Calculate the current drawn from the battery in the given network.
20. The following graph shows the variation of terminal potential difference V, across a combination of three
cells in series to a resistor, versus the current , I.
(i)Calculate the emf of e ach cell.
(ii)For what current I will the power dissipation of the circuit be maximum?
PRACTICAL BASE QUESTIONS:
1. Two students X and Y perform an experiment on potentiometer separately using the circuit.
Keeping other things unchanged
(i) X increases the value of distance R
(ii) Y decreases the value of resistance S in the set up.
How would these changes affect the position of null point
in each case and why?
2
For the potentiometer circuit shown in figure, points X and Y represent the two terminals of an unknown emf
E`. A student observed that when the jockey is moved from the end A to the end B of the potentiometer wire,
the deflection in the galvanometer remains in the same direction.
What may be the two possible faults in the circuit that could result in this observation?
If the galvanometer deflection at the end B is (i) more (ii) less, than that at the end A, which of two
faults, listed above, would be there in the circuit? Give reasons in support of your answer in each case.
3. Rama was performing an experiment to determine the internal resistance of a cell using a potentiometer set
up. After completing the circuit when the jockey was touched with two extreme ends of the wire the
deflection in the galvanometer was not reversed. He tried his level best to rectify the circuit to ensure both
side deflection of the galvanometer needle but could not succeed. Write point wise all the possible causes?
Long Answer Type Questions[5 marks each]
1.
(a) Describe the formula for the equivalent EMF and internal resistance for the parallel combination of
two cells with EMF E1 and E2 and internal resistances r1 and r2 respectively. What is the corresponding
formula for the series combination?
(b) Two cells of EMF 1V, 2V and internal resistances 2Ω and 1Ω respectively are connected in (i)
series, (ii) parallel. What should be the external resistance in the circuit so that the current through the
resistance be the same in the two cases? In which case more heat is generated in the cells?
2. Deduce the condition for balance in a Wheatstone bridge. Using the principle of Wheatstone bridge,
describe the method to determine the specific resistance of a wire in the laboratory. Draw the circuit
diagram and write the formula used. Write any two
precautions.
3. Describe the principle and construction of potentiometer. Explain how a potentiometer can be used to
compare the emfs of two primary cells?
4. Describe the principle and construction of potentiometer. Explain how a potentiometer can be used to find the
internal resistance of primary cells?
Value Based Questions
1. On July 30th 2012, India plunged into darkness due to overdrawing of power in some states. Vijay is
disturbed by this and carries out a survey to identify the causes of power loss in our country. He also
educates his neighbours on using electricity judiciously to save power.
(i) What values are reflected in Vijay’s behaviour?
(ii) What measures have the Government taken to fulfil the energy demands of people?
(iii) How can the people help the Government in their efforts?
2. Harish living in a village with his family had to take a old man, a victim of snake bite to the district
hospital 40 km away from his village for an immediate treatment to save his life. He found that the
battery of his bike was not working properly and the kick lever was also damaged. He removed the 6
V battery and fixed a 4 dry cell pack (1.5 V each) in place of the battery. The bike still did not start.
His younger brother Dadu was using a solar power lantern fitted with a 6 V storage battery ( lead
acid accumulator battery). He told his elder brother that the dry cells could not deliver the sufficient
current required to initiate ignition in the bike. Dadu brought his storage battery and helped his elder
brother Harish, to start the bike and take the patient to the city for treatment.
(i) List two qualities possessed by Harish and two qualities possessed by Dadu.
(ii) Why 4 dry cells of emf 1.5 V each were not able to supply the sufficient current required for
starting the bike?
(iii) Guess in which way he would have connected the dry cells to get the emf of 6 V.
3. TanviRastogi and AyushiSinha were performing an experiment to determine the internal resistance
of a cell using a potentiometer set up. After completing the circuit when the jockey was touched with
two extreme ends of the wire the deflection in the galvanometer was not reversed. They have tried
their level best to rectify the circuit to ensure both side deflection of the galvanometer needle but
could not succeed. In order to hurriedly complete the experiment Tanvi suggested that they will copy
and use the observations of the students of II batch. Ayushi however did not agree. She approached
the teacher for help. The teacher told them 3 possible causes of same sided deflection. Now Tanvi
and Ayushi completed the experiment and determine the value of internal resistance of cell using
l l
relation r = R 1 2 where, R is the resistance taken out of the resistance box, l1and l2are the
l2
balancing lengths when the key of the auxiliary circuit is open and closed respectively.
(i) What are the values possessed by Ayushi and Tanvi?
(ii) List the various causes for same sided deflection of galvanometer.
(iii) Can you suggest any other method to determine the internal resistance of the cell using a
potentionmeter?