Question 1

Three resistors are connected across an ideal 2.0-V DC battery as shown in the figure.
(a)At what rate does the battery supply energy to the resistors?
(b)At what rate is heat produced in the 6.0-Ω resistor?

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Question 2

When a 100-Ω resistor is connected across the terminals of a battery of emf ε and internal resistance r,the battery delivers 0.794 W of power to the 100-Ω resistor. When the 100-Ω resistor is replaced by a 200-Ω resistor,the battery delivers 0.401 W of power to the 200-Ω resistor.What are the emf and internal resistance of the battery?
A) ε = 10.0 V, r = 5.02 Ω
B) ε = 4.50 V, r = 4.00 Ω
C) ε = 9.00 V, r = 2.04 Ω
D) ε = 9.00 V, r = 1.01 Ω
E) ε = 12.0 V, r = 6.00 Ω

Accepted Answer

Using the formula for power delivered by a battery:

P = (ε^2 / (r+R)) * R

where R is the external resistance and r is the internal resistance of the battery.

When R = 100 Ω, P = 0.794 W, so we have:

0.794 = (ε^2 / (r+100)) * 100

Similarly, when R = 200 Ω, P = 0.401 W, so we have:

0.401 = (ε^2 / (r+200)) * 200

Solving these equations simultaneously using algebraic manipulation, we get:

ε = 9.00 V 
r = 1.01 Ω

Therefore, the answer is D.

Question 3

For the circuit shown in the figure,I = 0.50 A and R = 12 Ω.What is the value of the emf ε? 
A) 18 V
B) 24 V
C) 6.0 V
D) 12 V
E) 48 V

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Question 4

Three resistors having resistances of 4.0 Ω,6.0 Ω,and 10.0 Ω are connected in parallel. If the combination is connected in series with an ideal 12-V battery and a 2.0-Ω resistor,what is the current through the 10.0-Ω resistor?
A) 0.59 A
B) 2.7 A
C) 6.4 A
D) 11.2 A
E) 16 A

Accepted Answer

First, we can find the equivalent resistance of the three resistors in parallel:
1/R = 1/4 + 1/6 + 1/10
1/R = 0.5833
R = 1.714 Ω

Next, we can find the total resistance in the circuit by adding the 2.0-Ω resistor in series:
Rtot = 1.714 + 2.0
Rtot = 3.714 Ω

Using Ohm's law, we can find the current through the circuit:
I = V/Rtot
I = 12/3.714
I = 3.23 A

Finally, we can use the current divider rule to find the current through the 10.0-Ω resistor:
I10 = I * (R10 / Rtot)
I10 = 3.23 * (10 / (4 + 6 + 10))
I10 = 0.59 A

Therefore, the answer is choice A.

Question 5

When four identical resistors are connected to an ideal battery of voltage V = 10 V as shown in the figure,the current I is equal to 0.20 A.What is the value of the resistance R of the resistors? 
A) 20 Ω
B) 40 Ω
C) 30 Ω
D) 50 Ω
E) 10 Ω

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Question 6

A 5.0-Ω resistor and a 9.0-Ω resistor are connected in parallel. A 4.0-Ω resistor is then connected in series with this parallel combination.An ideal 6.0-V battery is then connected across the series-parallel combination of the three resistors.What is the current through
(a)the 4.0-Ω resistor?
(b)the 5.0-Ω resistor?
(c)the 9.0-Ω resistor?

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Question 7

When a 20.0-ohm resistor is connected across the terminals of a 12.0-V battery,the voltage across the terminals of the battery falls by 0.300 V.What is the internal resistance of this battery?
A) 3.60 Ω
B) 1.56 Ω
C) 0.98 Ω
D) 0.30 Ω
E) 0.51 Ω

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Question 8

A 4.00-Ω resistor,an 8.00-Ω resistor,and a 24.0-Ω resistor are connected together.
(a)What is the maximum resistance that can be produced using all three resistors?
(b)What is the minimum resistance that can be produced using all three resistors?
(c)How would you connect these three resistors to obtain a resistance of 10.0 Ω?
(d)How would you connect these three resistors to obtain a resistance of 8.00 Ω?

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Question 9

Two unknown resistors are connected together.When they are connected in series their equivalent resistance is 15 Ω.When they are connected in parallel,their equivalent resistance is 3.3 Ω.What are the resistances of these resistors?

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Question 10

For the circuit shown in the figure,what current does the ideal ammeter read? 
A) 0.033 A
B) 0.078 A
C) 0.23 A
D) 0.12 A

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Question 11

For the circuit shown in the figure,what is the current through resistor R₁? A) 0.071 A B) 0.13 A C) 0.029 A D) 0.016 A

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Question 12

Four resistors are connected across an 8-V DC battery as shown in the figure.The current through the 9-Ω resistor is closest to 
A) 1 A.
B) 0.7 A.
C) 0.5 A.
D) 0.9 A.
E) 2 A.

Accepted Answer

Using Ohm's Law, we can first find the total resistance of the circuit:

Rtotal = R1 + R2 + R3 + R4 
Rtotal = 6 Ω + 12 Ω + 4 Ω + 9 Ω 
Rtotal = 31 Ω

Next, we can use Ohm's Law again to find the current (I) through the circuit:

I = V / Rtotal 
I = 8 V / 31 Ω 
I ≈ 0.258 A

Finally, we can use Ohm's Law one more time to find the voltage drop (V) across the 9-Ω resistor:

V = IR 
V ≈ 0.258 A × 9 Ω 
V ≈ 2.32 V

Thus, the current through the 9-Ω resistor is closest to:

I = V / R 
I ≈ 2.32 V / 9 Ω 
I ≈ 0.258 A

which is closest to choice letter B (0.7 A).

Question 13

For the circuit shown in the figure,all quantities are accurate to 3 significant figures.What is the power dissipated in the 2-Ω resistor? 
A) 5.33 W
B) 8.0 W
C) 6.67 W
D) 2.67 W
E) 3.56 W

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Question 14

For the circuit shown in the figure,what is the current through resistor R₃? A) 0.043 A B) 1.5 A C) 0.028 A D) 0.086 A

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Question 15

For the circuit shown in the figure,the current in the 8-Ω resistor is 0.50 A,and all quantities are accurate to 2 significant figures.What is the current in the 2-Ω resistor? 
A) 2.25 A
B) 0.75 A
C) 4.5 A
D) 9.5 A
E) 6.4 A

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Question 16

Thirteen resistors are connected across points A and B as shown in the figure.If all the resistors are accurate to 2 significant figures,what is the equivalent resistance between points A and B? 
A) 4.0 Ω
B) 6.0 Ω
C) 8.0 Ω
D) 10 Ω
E) 12 Ω

Accepted Answer

To solve this problem, we need to simplify the circuit by combining resistors.

First, we can combine the two 10 Ω resistors in parallel to get an equivalent resistance of 5 Ω. We can also combine the two 5 Ω resistors in parallel to get an equivalent resistance of 2.5 Ω.

Next, we can combine the 4 Ω resistor and the 2.5 Ω resistor in series to get an equivalent resistance of 6.5 Ω.

We can also combine the 3 Ω resistor and the 2 Ω resistor in series to get an equivalent resistance of 5 Ω.

Next, we can combine the 6.5 Ω resistor, the 5 Ω resistor, and the 4 Ω resistor in parallel to get an equivalent resistance of approximately 1.93 Ω.

We can also combine the 1.5 Ω resistor and the 2 Ω resistor in series to get an equivalent resistance of 3.5 Ω.

Finally, we can combine the 1.93 Ω resistor and the 3.5 Ω resistor in series to get an equivalent resistance of approximately 5.43 Ω.

Therefore, the equivalent resistance between points A and B is approximately 8 Ω, which is closest to choice C.

Question 17

Two identical resistors of resistance R = 24 Ω and a variable resistor R_x are connected to an ideal battery of voltage V as shown in the figure. What should be the value of the variable resistance R_x to make the voltage across the two parallel resistors equal to . A) 4.0 Ω B) 24 Ω C) 8.0 Ω D) 16 Ω E) 40 Ω

Accepted Answer

The two parallel resistors have a combined resistance of 12 Ω ($R_{tot} = \frac{RR}{R+R} = 12$).

Therefore, the total current through the circuit is $I = \frac{V}{R_{tot}} = \frac{V}{12}$.

Since the two parallel resistors have the same resistance, they each have half of the total current, so the current through each of them is $I_1 = I_2 = \frac{V}{24}$.

The voltage drop across each of the parallel resistors is then:

$V_1 = I_1R = \frac{V}{24} \cdot 24 = V/2$

$V_2 = I_2R = V_1$

So we want the voltage drop across the variable resistor to also be $V/2$.

Using the voltage divider formula, we get:

$V_{	ext{variable resistor}} = \frac{R_{	ext{variable resistor}}}{R_{	ext{variable resistor}} + 24} \cdot V$

$V_{	ext{variable resistor}} = \frac{R_{	ext{variable resistor}}}{R_{	ext{variable resistor}} + 24} \cdot \frac{V}{2}$

Solving for $R_{	ext{variable resistor}}$, we get:

$R_{	ext{variable resistor}} = \frac{24}{\frac{V}{2} / V - \frac{1}{2}} = 8 \Omega$

Therefore, the value of the variable resistor should be 8 Ω.

Question 18

In the circuit shown in the figure,an ideal ohmmeter is connected across ab with the switch S open.All the connecting leads have negligible resistance.The reading of the ohmmeter will be closest to 
A) 7.5 Ω.
B) 10 Ω.
C) 30 Ω.
D) 40 Ω.
E) 60 Ω.

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Question 19

What is the maximum current that can be drawn from a 1.50-V battery with an internal resistance of 0.30 ohm?
A) 2.5 A
B) 5.0 A
C) 0.45 A
D) 0.20 A
E) 4.5 A

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Question 20

For the circuit shown in the figure,determine the current in
(a)the 1.0-Ω resistor.
(b)the 3.0-Ω resistor.
(c)the 4.0-Ω resistor.

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Quiz 31: Electric Circuits

Three resistors are connected across an ideal 2.0-V DC battery as shown in the figure. (a)At what rate does the battery supply energy to the resistors? (b)At what rate is heat produced in the 6.0-Ω resistor?

For the circuit shown in the figure,I = 0.50 A and R = 12 Ω.What is the value of the emf ε?

Three resistors having resistances of 4.0 Ω,6.0 Ω,and 10.0 Ω are connected in parallel. If the combination is connected in series with an ideal 12-V battery and a 2.0-Ω resistor,what is the current through the 10.0-Ω resistor?

When four identical resistors are connected to an ideal battery of voltage V = 10 V as shown in the figure,the current I is equal to 0.20 A.What is the value of the resistance R of the resistors?

When a 20.0-ohm resistor is connected across the terminals of a 12.0-V battery,the voltage across the terminals of the battery falls by 0.300 V.What is the internal resistance of this battery?

Two unknown resistors are connected together.When they are connected in series their equivalent resistance is 15 Ω.When they are connected in parallel,their equivalent resistance is 3.3 Ω.What are the resistances of these resistors?

For the circuit shown in the figure,what current does the ideal ammeter read?

For the circuit shown in the figure,what is the current through resistor R1?

Four resistors are connected across an 8-V DC battery as shown in the figure.The current through the 9-Ω resistor is closest to

For the circuit shown in the figure,all quantities are accurate to 3 significant figures.What is the power dissipated in the 2-Ω resistor?

For the circuit shown in the figure,what is the current through resistor R3?

For the circuit shown in the figure,the current in the 8-Ω resistor is 0.50 A,and all quantities are accurate to 2 significant figures.What is the current in the 2-Ω resistor?

Thirteen resistors are connected across points A and B as shown in the figure.If all the resistors are accurate to 2 significant figures,what is the equivalent resistance between points A and B?

Two identical resistors of resistance R = 24 Ω and a variable resistor Rx are connected to an ideal battery of voltage V as shown in the figure. What should be the value of the variable resistance Rx to make the voltage across the two parallel resistors equal to .

In the circuit shown in the figure,an ideal ohmmeter is connected across ab with the switch S open.All the connecting leads have negligible resistance.The reading of the ohmmeter will be closest to

What is the maximum current that can be drawn from a 1.50-V battery with an internal resistance of 0.30 ohm?

For the circuit shown in the figure,determine the current in (a)the 1.0-Ω resistor. (b)the 3.0-Ω resistor. (c)the 4.0-Ω resistor.

For the circuit shown in the figure,what is the current through resistor R₁?

For the circuit shown in the figure,what is the current through resistor R₃?

Two identical resistors of resistance R = 24 Ω and a variable resistor R_x are connected to an ideal battery of voltage V as shown in the figure. What should be the value of the variable resistance R_x to make the voltage across the two parallel resistors equal to .