WS: Series & Parallel Circuits (non-mixed) (AP1)
1. All resistors in the circuit are identical.
All batteries are ideal with voltages of
12V and 6 V as listed. All connecting
wires have negligible resistance.
 Rank in terms of total resistance
(Req) greatest to least. Justify your
ranking.
Largest Rtotal:
C
>
A
=
E
>
B
=
In series: The more resistors, the larger the resistance
In parallel, the more resistors, the smaller the resistance.
F
>
Smallest Rtotal:
D
2. Rank according to ammeter reading (current) from largest to smallest. All the light bulbs are
identical and can be treated as ohmic resistors. Assume the ammeter has zero resistance, the
batteries are ideal and the wires have zero resistance. Justify your reasoning.
a.
b.
A = B = C = Itotal
In series, current is the same
A = B = C = 1/3 Itotal
Only because the lightbulbs are the
same
B>A>C
small resistance  large current
See reasoning for #1
c.
d.
C>B>A
small resistance  large current
In parallel, the more resistors, the
smaller the resistance.
3. A student needs a 30  resistor, but all the stockroom has left is 10  resistors. Can the student
make a 30  resistor? If so, how? If not why not?
Put three 10 resistors in series. (Rtotal = 10 + 10 + 10 = 30)
4. If the multiple 10  resistors from the previous problem are hooked to a 12 V battery, what is the
current through each resistor and the voltage of each resistor? (0.4A; 4V)
Itotal =
∆Vtotal
=
Rtotal
12V
30Ω
= 𝟎. 𝟒𝐀
V10Ω = I10Ω R10Ω = (0.4A)(10Ω) = 𝟒𝐕
Current is the same in series
All the resistors are the same, so they all have the same
voltage.
5. A student needs a 1.0  resistor, but all the stockroom has left is 4  resistors. Can the student
make a 1.0  resistor? If so how, if not why not?
𝟏
𝟏
𝟏
𝟏
𝟏
Put four 4  resistors in parallel.
=
+
+
+
𝑹
𝟒
𝟒
𝟒
𝟒
𝒕𝒐𝒕𝒂𝒍
6. If the multiple 4  resistors from the previous problem are hooked to a 12 V battery, what is the
current through and voltage across each resistor? (3A; 12V)
V = 12V (they are in parallel with the battery and in parallel voltage is the same.)
I4Ω =
∆V4Ω
R4Ω
=
12V
4Ω
= 𝟑𝐀 All the resistors are the same, so they all have the same current.
7. A series circuit is made from a 3.0 , 6.0 , and 9.0  resistors hooked to a 24 V battery.
a. Draw the circuit
b. What is the total resistance for the circuit? (18)
c. What is the power output of each resistor? (5.3W,11W,16W)
Rtotal = 3 + 6 + 9 = 18 
𝐼𝑡𝑜𝑡𝑎𝑙 =
∆𝑉𝑡𝑜𝑡𝑎𝑙 24𝑉
=
= 1.33𝐴
𝑅𝑡𝑜𝑡𝑎𝑙
18Ω
2
𝑃3Ω = 𝐼3Ω
𝑅3Ω = (1.33𝐴)2 (3Ω) = 5.3W
2
𝑃6Ω = 𝐼6Ω
𝑅6Ω = (1.33𝐴)2 (6Ω) = 11𝑊
2
𝑃9Ω = 𝐼9Ω 𝑅9Ω = (1.33𝐴)2 (9Ω) = 16W
8. A 12  and 15  resistors are hooked up in series with a 9.0 V battery. What is the power
dissipated by each resistor? (1.3 W; 1.7 W)
Rtotal = 12 + 15 = 27 
𝐼𝑡𝑜𝑡𝑎𝑙 =
∆𝑉𝑡𝑜𝑡𝑎𝑙
9𝑉
=
= 0.33𝐴
𝑅𝑡𝑜𝑡𝑎𝑙
27Ω
2
𝑃12Ω = 𝐼12Ω
𝑅12Ω = (0.33𝐴)2 (12Ω) = 1.3W
2
𝑃15Ω = 𝐼15Ω
𝑅15Ω = (0.33𝐴)2 (15Ω) = 1.7𝑊
9. A parallel circuit is made up of three resistors (3.0 , 6.0 , and 9.0 and connected to a 24 V
battery.
a. Draw the circuit
b. What is the total resistance for the circuit? (1.6)
c. What is the power output of each resistor? (192W, 96W, 64W)
1
1
1
1
=
+
+
𝑅𝑡𝑜𝑡𝑎𝑙 3Ω 6Ω 9Ω
1
6
3
2
=
+
+
𝑅𝑡𝑜𝑡𝑎𝑙 18Ω 18Ω 18Ω
1
11
=
→ 𝑅𝑡𝑜𝑡𝑎𝑙 = 1.6Ω
𝑅𝑡𝑜𝑡𝑎𝑙 18
Voltage is the same in Parallel
2
𝑉3Ω
24𝑉 2
𝑃3Ω =
=
= 192𝑊
𝑅3Ω
3Ω
𝑃6Ω =
𝑃9Ω
2
𝑉6Ω
24𝑉 2
=
= 96𝑊
𝑅6Ω
6Ω
2
𝑉9Ω
24𝑉 2
=
=
= 64𝑊
𝑅9Ω
9Ω