Series Circuits
Solutions to p19
1. Three 20 W resistors are connected in series across a 120 V generator. What current flows in the circuit?
Rt = 20 + 20 + 20 = 60 W.
Vt = I Rt
120 = I
(60)
I = 2 A.
2. Ten Christmas lights have equal resistances. When connected to a 120 V outlet, a current of 0.5 A flows through the bulbs. What is the resistance of just one bulb?
Vt = I Rt
120 = 0.5 Rt
Rt = 240 W.
Each light bulb will have 240/10 lights = 24 W.
3. A lamp with a resistance of 10 W is connected across a 12 V battery. What resistance must be connected to the lamp to create a current of 0.5 A?
Vt = I Rt
12 = 0.5
Rt
Rt = 24 W.
R + Rlamp = 24
R = 24 -10 = 14 W.
4. A 20 W resistor and a 30 W resistor are connected in series and placed across a potential difference of 100 V. Find the voltage drop across each resistor.
Vt = I Rt
100 = I (20
+ 30)
I = 2 A
V1
= I R1.
= 2(20) =
40 V
V2
= I R2.
= 2(30) = 60 V
5. Find the voltage across each resistor, as well as the total voltage.
a.
30 W A 0.10 A
50 W
V1 = 0.10 (30) = 3 V
V2 = 0.10 (50) = 5 V
Vt = 3 + 5 = 8 V
b.
10 W A 0.10 A
40W
20 W
V1 = 0.10 (10) = 1 V
V2 = 0.10 (20) = 2 V
V3 = 0.10 (40) = 4 V
Vt = 7 V
6. Find the current as well as the voltage across each resistor.
a.
30 W A
80 V
50 W
Vt = I Rt
80 = I (30
+ 50)
I = 1 A
V1
= 1 (30) = 30 V
V2 = 1 (50) = 50 V
b.
100 W A
120 V
150 W
Vt = I Rt
120 = I
(100 + 150)
I = 0.48 A
V1
= 0.48 (100) = 48 V
V2 = 0.48 (150) = 72 V
c.
60V 100 W A
80W
20 W
Vt = I Rt
60 = I (100
+ 20+ 80)
I = 0.30 A
V1
= 0.30 (100) = 30 V
V2 = 0.30 (20) = 6 V
V3 = 0.30 (80) = 24 V
V=5
7.
??? W A 2.0 A
??? V
2 W
In the above diagram, find the total voltage and the missing resistance.
V2 = I R2 = 2 (2) = 4 V
Vt = 5 + 4 = 9 V
R1 = V1/I = 5/2 = 2.5 W.
8. Three known resistances are connected in series
to the terminals of a power source. The
potential difference at the terminals of the 3.0 W
resistance is 12 V.
a. What
is the potential difference of the power source?
I = 12V/3.0W = 4.0 A
Vt = IRt
= 4.0 (2 + 3 + 4) = 36 V
b. What
is the voltage drop across the 4.0 W resistor?
V3 = 4.0(4.0) = 16 V
c. What
is the voltage drop across the 2.0 W resistor?
8.0 V
9. Use
the diagram to your right, where V1 = 12 V; V2 = 5.0 V.
a. What is the
reading on voltmeter V3?
V1 = Vt = V2 + V3
12 = 5.0 + V3
V3 = 7.0 V
b. If the current flowing out of the battery was 125 mA, what would be the value of R2?
125 mA = 0.125 A
V2
= IR2.
5.0 = 0.125 R2.
R2
= 40 W.
10. Flashback
In an electric circuit, the potential
difference across the terminals of a resistor was set at different levels and
the resulting current intensity was measured.
The measurements are recorded in the table below.
|
Potential Difference V (V) |
Current Intensity I (A) |
|
0 |
0 |
|
5 |
1.0 |
|
20 |
4.1 |
|
35 |
7.1 |
|
40 |
8.1 |
Draw a graph using the above data
and then use the graph to determine the resistance of this resistor.
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5 10 15 20 25 30 35 40
Voltage(V)
Note
although the following seems to involve extra work, it is important to place V
on the x axis because of the ay the experiment was done (that’s why V is in the
first column; it is the independent variable: what we actually controlled in
the experiment)
Slope
= (6-2)/(30-10)= I/V = G =0.20 S
R =
1/G = 1/0.20 = 5.0 W.