Question 1

What is the equivalent resistance between points A and B of the network shown in the figure?

Accepted Answer

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Question 2

A combination of a 2.0-Ω resistor in series with 4.0-Ω resistor is connected in parallel with a 3.0-Ω resistor. What is the equivalent resistance of this system?
A) 2.0 Ω
B) 3.0 Ω
C) 4.0 Ω
D) 9.0 Ω

Accepted Answer

The equivalent resistance of resistors in series (2.0 Ω and 4.0 Ω) is their sum, which is 6.0 Ω. This 6.0-Ω combination is then in parallel with a 3.0-Ω resistor. The equivalent resistance for parallel resistors is given by 1/Req = 1/R1 + 1/R2. Thus, 1/Req = 1/6 + 1/3 = 1/2, making Req = 2.0 Ω.

Question 3

A group of 1.0-μF, 2.0-μF, and 3.0-μF capacitors is connected in parallel across a 24-V potential difference (a battery). How much energy is stored in this three-capacitor combination when the capacitors are fully charged?
A) 1.7 mJ
B) 2.1 mJ
C) 4.8 mJ
D) 7.1 mJ

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Question 4

The network shown is assembled with uncharged capacitors X , Y, and Z, with C_X=3.0 $\mu$F, C_Y=5.0$\mu$F and C_Z=1.0 $\mu$F The switches S₁ and S₂ are initially open, and a potential difference V_ab = 120 V is applied between points a and b. After the network is assembled, switch S₁ is then closed, but switch S₂ is kept open. What is the final potential difference across capacitor Z? A) 100 V B) 600 V C) 55 V D) 38 V E) 29 V

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Question 5

Two 4.0-Ω resistors are connected in parallel, and this combination is connected in series with 3.0 Ω. What is the equivalent resistance of this system?
A) 1.2 Ω
B) 5.0 Ω
C) 7.0 Ω
D) 11 Ω

Accepted Answer

The equivalent resistance of two resistors in parallel is given by:
1/Req = 1/R1 + 1/R2
1/Req = 1/4 + 1/4
1/Req = 1/2
Req = 2 Ω
The equivalent resistance of the entire circuit can now be found by adding the two resistances in series:
Req = 2 Ω + 3 Ω
Req = 5 Ω

Question 6

What resistance must be connected in parallel with a 633-Ω resistor to produce an equivalent resistance of 205 Ω?

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Question 7

A 2.0-Ω resistor is in series with a parallel combination of 4.0-Ω, 6.0-Ω, and 12-Ω resistors. What is the equivalent resistance of this system?
A) 24 Ω
B) 4.0 Ω
C) 1.8 Ω
D) 2.7 Ω

Accepted Answer

The equivalent resistance of the parallel combination of 4.0-Ω, 6.0-Ω, and 12-Ω resistors is:
1/Req = 1/4 + 1/6 + 1/12
1/Req = 1/2
Req = 2.0 Ω
Therefore, the total equivalent resistance is:
R = 2.0 Ω + 2.0 Ω
R = 4.0 Ω

Question 8

Three 2.0-Ω resistors are connected to form the sides of an equilateral triangle ABC as shown in the figure. What is the equivalent resistance between any two points, AB, BC, or AC, of this circuit? 
A) 2.0 Ω
B) 6.0 Ω
C) 4.3 Ω
D) 3.3 Ω
E) 1.3 Ω

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Question 9

The capacitive network shown in the figure is assembled with initially uncharged capacitors. Assume that all the quantities in the figure are accurate to two significant figures. The switch S in the network is kept open throughout. What is the total energy stored in the seven capacitors? 
A) 48 mJ
B) 72 mJ
C) 96 mJ
D) 120 mJ
E) 144 mJ

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Question 10

The network shown is assembled with uncharged capacitors X , Y, and Z, with C_X=3.0 $\mu$F, C_Y=5.0$\mu$F and C_Z=1.0 $\mu$F The switches S₁ and S₂ are initially open, and a potential difference V_ab = 120 V is applied between points a and b. After the network is assembled, switch S₁ is then closed, but switch S₂ is kept open. How much charge is finally stored in capacitor Y? A) 110 µC B) 54 µC C) 81 µC D) 140 µC E) 160 µC

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Question 11

The network shown is assembled with uncharged capacitors X , Y, and Z, with C_X = 4.0 μF, C_Y = 6.0 μF, and C_Z = 5.0 μF. The switches S₁ and S₂ are initially open, and a potential difference V_ab = 120 V is applied between points a and b. After the network is assembled, switch S₁ is then closed, but switch S₂ is kept open. What is the final potential difference across capacitor X? A) 120 V B) 82 V C) 75 V D) 67 V E) 60 V

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Question 12

A 9.00-µF and a 12.0-µF capacitor are connected together, and this combination is connected across a 25.0-V potential difference. How much electric energy is stored in the combination if they are connected (a) in parallel or (b) in series?

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Question 13

Five 2.0-Ω resistors are connected as shown in the figure. What is the equivalent resistance of this combination between points a and b? 
A) 1.0 Ω
B) 10.0 Ω
C) 2.0 Ω
D) 6.0 Ω
E) 0.40 Ω

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Question 14

Two resistors in series are equivalent to 9.0 Ω, and in parallel they are equivalent to 2.0 Ω. What are the resistances of these two resistors?

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Question 15

The resistors in the circuit shown in the figure each have a resistance of $700 \Omega$ What is the equivalent resistance between points a and b of this combination? 
A) 700 Ω
B) 2800 Ω
C) 175 Ω
D) 1400 Ω

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Question 16

What different resistances can be obtained by using two 2.0-Ω resistors and one 4.0-Ω resistor? You must use all three of them in each possible combination.

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Question 17

What is the equivalent resistance in the circuit shown in the figure? 
A) 80 Ω
B) 55 Ω
C) 50 Ω
D) 35 Ω

Accepted Answer

To calculate the equivalent resistance, first we can simplify the circuit by combining the three resistors in parallel. The equivalent resistance of 6 Ω, 12 Ω, and 18 Ω in parallel is:

1/Req = 1/6 + 1/12 + 1/18 
1/Req = 1/3 
Req = 3 Ω

Now we have two resistors in series with each other, which we can add together to find the total equivalent resistance:

Req = 3 + 47 = 50 Ω

Therefore, the answer is C, 50 Ω.

Question 18

Three capacitors are arranged as shown in the figure, with a voltage source connected across the combination. C₁ has a capacitance of $9.0 \mathrm { pF }$ $C _ { 2 }$ has a capacitance of $18.0 \mathrm { pF } \text {, }$ and $C _ { 3 }$ has a capacitance of $27.0 \mathrm { pF }$ Find the potential drop across the entire arrangement if the potential drop across C₂ is $257.0 \mathrm {~V}$ A) 1500 V B) 1000 V C) 470 V D) 430 V

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Question 19

The network shown is assembled with uncharged capacitors X , Y, and Z, with $C X = 4.0 \mu \mathrm { F }$ $\mathrm { CY } = 3.0 \mu \mathrm { F }$ and $C Z = 5.0 \mu \mathrm { F }$ The switches S₁ and S₂ are initially open, and a potential difference V_ab = 120 V is applied between points a and b. After the network is assembled, switch S₁ is then closed, but switch S₂ is kept open. How much energy is finally stored in capacitor X? A) 29 mJ B) 0.48 mJ C) 0.24 mJ D) 58 mJ E) 0.96 mJ

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Question 20

Each of the resistors shown in the figure has a resistance of $180.0 \Omega$
 What is the equivalent resistance between points a and b of this combination? 
A) 450.0 Ω
B) 720.0 Ω
C) 540.0 Ω
D) 180.0 Ω

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Quiz 23: Circuits

What is the equivalent resistance between points A and B of the network shown in the figure?

A combination of a 2.0-Ω resistor in series with 4.0-Ω resistor is connected in parallel with a 3.0-Ω resistor. What is the equivalent resistance of this system?

A group of 1.0-μF, 2.0-μF, and 3.0-μF capacitors is connected in parallel across a 24-V potential difference (a battery) . How much energy is stored in this three-capacitor combination when the capacitors are fully charged?

Two 4.0-Ω resistors are connected in parallel, and this combination is connected in series with 3.0 Ω. What is the equivalent resistance of this system?

What resistance must be connected in parallel with a 633-Ω resistor to produce an equivalent resistance of 205 Ω?

A 2.0-Ω resistor is in series with a parallel combination of 4.0-Ω, 6.0-Ω, and 12-Ω resistors. What is the equivalent resistance of this system?

Three 2.0-Ω resistors are connected to form the sides of an equilateral triangle ABC as shown in the figure. What is the equivalent resistance between any two points, AB, BC, or AC, of this circuit?

The capacitive network shown in the figure is assembled with initially uncharged capacitors. Assume that all the quantities in the figure are accurate to two significant figures. The switch S in the network is kept open throughout. What is the total energy stored in the seven capacitors?

A 9.00-µF and a 12.0-µF capacitor are connected together, and this combination is connected across a 25.0-V potential difference. How much electric energy is stored in the combination if they are connected (a) in parallel or (b) in series?

Five 2.0-Ω resistors are connected as shown in the figure. What is the equivalent resistance of this combination between points a and b?

Two resistors in series are equivalent to 9.0 Ω, and in parallel they are equivalent to 2.0 Ω. What are the resistances of these two resistors?

What different resistances can be obtained by using two 2.0-Ω resistors and one 4.0-Ω resistor? You must use all three of them in each possible combination.

What is the equivalent resistance in the circuit shown in the figure?

Quiz 23: Circuits

What is the equivalent resistance between points A and B of the network shown in the figure?

A combination of a 2.0-Ω resistor in series with 4.0-Ω resistor is connected in parallel with a 3.0-Ω resistor. What is the equivalent resistance of this system?

A group of 1.0-μF, 2.0-μF, and 3.0-μF capacitors is connected in parallel across a 24-V potential difference (a battery) . How much energy is stored in this three-capacitor combination when the capacitors are fully charged?

Two 4.0-Ω resistors are connected in parallel, and this combination is connected in series with 3.0 Ω. What is the equivalent resistance of this system?

What resistance must be connected in parallel with a 633-Ω resistor to produce an equivalent resistance of 205 Ω?

A 2.0-Ω resistor is in series with a parallel combination of 4.0-Ω, 6.0-Ω, and 12-Ω resistors. What is the equivalent resistance of this system?

Three 2.0-Ω resistors are connected to form the sides of an equilateral triangle ABC as shown in the figure. What is the equivalent resistance between any two points, AB, BC, or AC, of this circuit?

The capacitive network shown in the figure is assembled with initially uncharged capacitors. Assume that all the quantities in the figure are accurate to two significant figures. The switch S in the network is kept open throughout. What is the total energy stored in the seven capacitors?

A 9.00-µF and a 12.0-µF capacitor are connected together, and this combination is connected across a 25.0-V potential difference. How much electric energy is stored in the combination if they are connected (a) in parallel or (b) in series?

Five 2.0-Ω resistors are connected as shown in the figure. What is the equivalent resistance of this combination between points a and b?

Two resistors in series are equivalent to 9.0 Ω, and in parallel they are equivalent to 2.0 Ω. What are the resistances of these two resistors?

The resistors in the circuit shown in the figure each have a resistance of 700Ω700 \Omega700Ω What is the equivalent resistance between points a and b of this combination?

What different resistances can be obtained by using two 2.0-Ω resistors and one 4.0-Ω resistor? You must use all three of them in each possible combination.

What is the equivalent resistance in the circuit shown in the figure?

Each of the resistors shown in the figure has a resistance of 180.0Ω180.0 \Omega180.0Ω What is the equivalent resistance between points a and b of this combination?