Question 1

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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Question 2

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 3

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

The circuit can be simplified by combining the resistors in parallel and series. Starting from the right side of the circuit, the two 4 Ω resistors are in parallel, resulting in an equivalent resistance of 2 Ω. Moving to the left, the two 6 Ω resistors are also in parallel, resulting in an equivalent resistance of 3 Ω. The combination of the 2 Ω and 3 Ω resistors is then in series with the 5 Ω resistor, resulting in an equivalent resistance of 10 Ω. Continuing to the left, the two 3 Ω resistors and the 5 Ω resistor are in parallel, resulting in an equivalent resistance of 1.875 Ω. Finally, the 2 Ω and 1.875 Ω resistors are in series, resulting in an equivalent resistance of 3.875 Ω. Rounding to 2 significant figures, the answer is 8.0 Ω.

Question 4

The emf and the internal resistance of a battery are shown in the figure.If a current of 7.8 A is established through the battery from b to a,what is the terminal voltage V_ab of the battery? A)-30 V B)80 V C)30 V D)-80 V E)zero

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Question 5

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 6

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 7

The heater element of a particular 120-V toaster is a 8.9-m length of nichrome wire,whose diameter is 0.86 mm.The resistivity of nichrome at the operating temperature of the toaster is 1.3 × 10^-6 Ω ∙ m.If the toaster is operated at a voltage of 120 V,how much power does it draw? A)720 W B)700 W C)750 W D)770 W E)800 W

Accepted Answer

First, calculate the resistance of the nichrome wire using the formula $R = \rho \frac{L}{A}$, where $\rho$ is the resistivity, $L$ is the length, and $A$ is the cross-sectional area of the wire. The area $A$ can be found using the formula for the area of a circle, $A = \pi r^2$, where $r$ is the radius of the wire. Given the diameter is 0.86 mm, the radius is 0.43 mm or 0.43 x 10^-3 m. Thus, $A = \pi (0.43 \times 10^{-3})^2$. Plugging in the values, $R = 1.3 \times 10^{-6} \Omega \cdot m \times \frac{8.9}{\pi (0.43 \times 10^{-3})^2}$. After calculating $R$, use the power formula $P = \frac{V^2}{R}$ with $V = 120$ V to find the power $P$. The calculation yields approximately 720 W.

Question 8

In the figure a current of 6.0 A is drawn from the battery.What is the terminal voltage V_ab of the battery? A)0.00 V B)+12 V C)+24 V D)-12 V E)-24 V

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Question 9

The emf and the internal resistance of a battery are as shown in the figure.If a current of 8.3 A is drawn from the battery when a resistor R is connected across the terminals ab of the battery,what is the power dissipated by the resistor R? 
A)440 W
B)700 W
C)620 W
D)530 W
E)790 W

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Question 10

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 11

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 12

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 parallel combination of resistors:
1/R = 1/4 + 1/6 + 1/10
1/R = 0.45
R = 2.2 Ω

Then, we can find the total resistance of the circuit in series:
R_total = R_par + 2
R_total = 4.2 Ω

Using Ohm's Law, we can find the current through the circuit:
I = V/R
I = 12/4.2
I = 2.857 A

We can then use the current divider rule to find the current through the 10 Ω resistor:
I_10 = (10/20.0) * 2.857
I_10 = 0.571 A

Rounding to two significant figures, we get 0.59 A, which is answer choice A).

Question 13

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 14

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 15

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

Since the resistors are in parallel, the equivalent resistance can be found as
1/R = 1/10 + 1/12 + 1/15 + 1/9
R = 3.202 Ω
Using Ohm's Law, the current through the 9-Ω resistor can be found as
I = V/R = 8 V / 3.202 Ω = 2.495 A 
However, since the 9-Ω resistor is connected in parallel with the 15-Ω resistor, most of the current will flow through the 15-Ω resistor, leaving less current through the 9-Ω resistor. We can estimate the current through the 9-Ω resistor as the total current (8 V / 3.202 Ω = 2.495 A) times the fraction of the total resistance contributed by the 9-Ω resistor (9 Ω / (10 Ω + 12 Ω + 15 Ω + 9 Ω) = 0.225). Therefore, the current through the 9-Ω resistor is approximately 2.495 A x 0.225 = 0.561 A, which is closest to choice B, 0.7 A.

Question 16

In the figure,when the terminal voltage V_ab of the battery is equal to 20 V,how much current passes through the battery,including its direction? A)4 A,from a to b B)5 A,from a to b C)6 A,from a to b D)4 A,from b to a E)5 A,from b to a

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Question 17

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 18

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

Since the two resistors are identical, the voltage across each of them is equal. Let's call this voltage V1. The voltage across the variable resistor (R_x) is then V-V1. The total resistance of the circuit can be calculated using the formula: $R_{tot} = R + R_{parallel}$ where R is the resistance of one of the identical resistors, and $R_{parallel}$ is the total resistance of the two resistors in parallel. We can calculate $R_{parallel}$ using the formula: $\frac{1}{R_{parallel}} = \frac{1}{R} + \frac{1}{R}$ Simplifying this, we get: $R_{parallel} = \frac{R}{2}$ So the total resistance becomes: $R_{tot} = R + \frac{R}{2} = \frac{3R}{2}$ The current in the circuit can be calculated using Ohm's Law: $I = \frac{V}{R_{tot}}$ The current through each of the identical resistors is then: $I_1 = \frac{V_1}{R} = \frac{V}{2R_{tot}}$ The voltage across the variable resistor can now be calculated using Ohm's Law again: $V-V_1 = I_1R_x$ Substituting the expressions for $I_1$ and $R_{tot}$, we get: $V-V_1 = \frac{VR_x}{3R}$ We know that $V_1 = 11eab929_294a_3cb9_99e6_81f4fcb9fe96_TB4470_00$. Substituting this, and simplifying, we get: $V-V_1 = \frac{8V}{9}$ So the variable resistor needs to have a resistance of: $R_x = \frac{8V}{9} imes \frac{R}{V} = \frac{8R}{9} = 8 \Omega$ Therefore, the answer is C) 8.0 Ω.

Question 19

The emf and the internal resistance of a battery are as shown in the figure.When the terminal voltage V_ab is equal to 17.4 V,what is the current through the battery,including its direction? A)6.8 A,from b to a B)8.7 A,from b to a C)6.8 A,from a to b D)8.7 A,from a to b E)16 A,from b to a

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Question 20

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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Quiz 28: Fundamentals of Circuits

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,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?

The emf and the internal resistance of a battery are shown in the figure.If a current of 7.8 A is established through the battery from b to a,what is the terminal voltage Vab of the battery?

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

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?

The heater element of a particular 120-V toaster is a 8.9-m length of nichrome wire,whose diameter is 0.86 mm.The resistivity of nichrome at the operating temperature of the toaster is 1.3 × 10-6 Ω ∙ m.If the toaster is operated at a voltage of 120 V,how much power does it draw?

In the figure a current of 6.0 A is drawn from the battery.What is the terminal voltage Vab of the battery?

The emf and the internal resistance of a battery are as shown in the figure.If a current of 8.3 A is drawn from the battery when a resistor R is connected across the terminals ab of the battery,what is the power dissipated by the resistor R?

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?

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?

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?

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

In the figure,when the terminal voltage Vab of the battery is equal to 20 V,how much current passes through the battery,including its direction?

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

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 .

The emf and the internal resistance of a battery are as shown in the figure.When the terminal voltage Vab is equal to 17.4 V,what is the current through the battery,including its direction?

The emf and the internal resistance of a battery are shown in the figure.If a current of 7.8 A is established through the battery from b to a,what is the terminal voltage V_ab of the battery?

The heater element of a particular 120-V toaster is a 8.9-m length of nichrome wire,whose diameter is 0.86 mm.The resistivity of nichrome at the operating temperature of the toaster is 1.3 × 10^-6 Ω ∙ m.If the toaster is operated at a voltage of 120 V,how much power does it draw?

In the figure a current of 6.0 A is drawn from the battery.What is the terminal voltage V_ab of the battery?

In the figure,when the terminal voltage V_ab of the battery is equal to 20 V,how much current passes through the battery,including its direction?

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 .

The emf and the internal resistance of a battery are as shown in the figure.When the terminal voltage V_ab is equal to 17.4 V,what is the current through the battery,including its direction?