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DC Circuits Study Guide
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Batteries
1. What is a battery
2. Basic concepts of batteries
3. How do battery voltages add in various configurations (series, parallel, complex)
4. Batteries maintain constant voltage. The current can vary as necessary.
DC Circuit Basics
1. Definition of current
2. Ohm’s Law
3. Resistance of a conductor
4. Power in a circuit. Power of a resistor.
5. Use of voltmeters and ammeters
Series and Parallel Circuits
1. Adding resistors in parallel.
2. Adding resistors in series.
3. Combination circuits.
-----------------------------------------------------------------------------------------------------Practice problems.
150V
9Ω
9Ω
B
9Ω
A
1.
2.
3.
4.
5.
9Ω
Find the equivalent resistance of the above circuit.
How much current is drawn by the circuit?
How much power is drawn by the overall circuit?
How much power is drawn by the resistor labeled as A in the above circuit?
For the resistor labeled B, draw a circuit diagram that includes a voltmeter and ammeter, showing
how you would modify the circuit to measure voltage and current.
6. A light bulb is plugged into a 120-volt outlet and has a 0.7 A current in it. What is the power
rating of the light bulb?
7. Consider two copper wires. One has twice the length and twice the cross-sectional area of the
other. How do the resistances of these two wires compare?
8. A resistor is hooked up to a battery. If the value of the resistance is doubled, what happens to the
voltage, current, and power drawn from the battery?
9. If you double the length of a resistor and decrease its area by a factor of 2, what happens to the
overall resistance?
10. What is the power dissipated by a toaster that has a resistance of 40 ohms and is plugged into a
120-V outlet?
11. There are three resistors: 10Ω, 20Ω, and 30Ω. What is the largest resistance that you can get by
hooking them together? How would you do that? What is the smallest resistance that you can get
by hooking them together? How would you do that?
12. How many total coulombs of charge pass through a resistor if a current of .5A runs through it for
20s?
DC Circuits Study Guide
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-----------------------------Answers-----------------------------------------------------------------
18Ω
9Ω
150V
9Ω
B
9Ω
B
150V
9Ω
A
series
RT  9  9  18
9Ω
A
9Ω
parallel
1
1 1 3 1
  

RT 18 9 18 6
150V
6Ω
150V
series
A 9Ω
1.
2.
RT  6  9  15
15Ω
Find the equivalent resistance of the above circuit. (See above)
First combine resistors in series, then combine resistors in parallel, finally combines resistors in
series. Answer 15Ω.
How much current is drawn by the circuit?
V  IR so I 
V 150

 10 Amps
R 15
3.
How much power is drawn by the overall circuit?
4.
How much power is drawn by the resistor labeled as A in the above circuit?
P  IV  10 A 150V  1500W (Watts)
P  IV  I 2 R  10 2 * 9  900W
5. A light bulb is plugged into a 120-volt outlet and has a 0.7 A current in it. What is the
power rating of the light bulb?
P  IV  0.7 *120  84W
DC Circuits Study Guide
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6. For the resistor labeled B, draw a circuit diagram that includes a voltmeter and ammeter, showing
how you would modify the circuit to measure voltage and current.
9Ω
150V
9Ω
B
9Ω
V
A
A
9Ω
Note that
a) The voltmeter is hooked up in parallel with the resistor.
b) The ammeter is hooked up in series with the resistor. That means that the circuit has to be opened up
for the ammeter to be inserted in series.
7.
Consider two copper wires. One has twice the length and twice the cross-sectional area of the
other. How do the resistances of these two wires compare?
R
L
A
so : R1 
L1
A1
and R 2 
L2
A2

 2 L1 
2 A1 
The 2' s cancel so R 2  R1
8.
A resistor is hooked up to a battery. If the value of the resistance is doubled, what happens to the
voltage, current, and power drawn from the battery?
a) Voltage does not change. A battery maintains the voltage constant.
b) Since resistance increases and voltage stays constant, the current is reduced. According to
Ohm’s Law:
V
V  IR so I  . So if R doubles, I decreases by a factor of 2.
R
c) Power decreases:
9.
If you double the length of a resistor and decrease its area by a factor of 2, what happens to the
overall resistance? (See #7)
P  IV
so : R1 
L1
A1
and R 2 
L2
A2

 2 L1 
 A 


 2L 1 
4
L1
A1
so : R 2  4 R1
DC Circuits Study Guide
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10. What is the power dissipated by a toaster that has a resistance of 40 ohms and is plugged into a
120-V outlet?
P  IV
V2
V 
but V  IR so P   V 
R
R
2
2
V
120
P

 360W
R
40
11. There are three resistors: 10Ω, 20Ω, and 30Ω. What is the largest resistance that you can get by
hooking them together? How would you do that? What is the smallest resistance that you can get
by hooking them together? How would you do that?
Largest: Add in series:
RT  R1  R2  R3  10  20  30  60
Smallest: Add in parallel:
1
1
1
1
1 1
1
 

  
RT R1 R2 R3 10 20 30
1
 0.1  0.05  0.033  .183
RT
1
RT 
 5.5
.183
12. How many total coulombs of charge pass through a resistor if a current of .5A runs through it for
20s?
I
Q
so Q  I  t  0.5  20  10C
t