Question 1

A charged capacitor is connected in series with a resistor and an open switch. At time t = 0 s, the switch is closed. Which of the graphs below best describes the potential difference V across the capacitor as a function of time t? 
A)

B)

C)

D)

E)

Accepted Answer

The answer of A charged capacitor is connected in series...

Question 2

A charged capacitor is connected in series with a resistor and an open switch. At time t = 0 s, the switch is closed. Which of the graphs below best describes the potential difference V across the resistor as a function of time t? 
A)

B)

C)

D)

E)

Accepted Answer

- Initially, when the switch is closed, the capacitor is fully charged and acts as a voltage source, while the resistor acts as a load. Therefore, the potential difference across the resistor will initially be equal to the voltage across the capacitor.
- As time passes, the capacitor will start to discharge through the resistor, resulting in a decrease in the potential difference across the resistor. The rate of decrease will be dictated by the time constant RC, where R is the resistance and C is the capacitance of the circuit. 
- The potential difference across the resistor will eventually reach zero once the capacitor is fully discharged, which will take approximately 5 time constants. Therefore, the graph that best represents this scenario is option B.

Question 3

A resistor is made out of a wire having a length L. When the ends of the wire are attached across the terminals of an ideal battery having a constant voltage V₀ across its terminals, a current I flows through the wire. If the wire were cut in half, making two wires of length L/2, and both wires were attached across the terminals of the battery (the right ends of both wires attached to one terminal, and the left ends attached to the other terminal), how much current would the battery put out? A) 4I B) 2I C) I D) I/2 E) I/4

Accepted Answer

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Question 4

Identical light bulbs can be attached to identical ideal batteries in three different ways (A, B, orC), as shown in the figure. The ranking (from lowest to highest) of the total power produced by the battery is

A) B, A, C
B) A, B, C
C) C, B, A
D) A, C, B

Accepted Answer

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Question 5

For the circuit shown in the figure, write the Kirchhoff loop equation for the entire outside loop. Notice the directions of the currents!

Accepted Answer

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Question 6

A charged capacitor is connected in series with a resistor and an open switch. At time t = 0 s, the switch is closed. Which of the graphs below best describes the current I through the resistor as a function of time t? 
A)

B)

C)

D)

E)

Accepted Answer

The answer of A charged capacitor is connected in series...

Question 7

In the circuit shown in the figure, the resistor R has a variable resistance. As R is decreased, what happens to the currents? A) I₁ remains unchanged and I₂ increases. B) I₁ decreases and I₂ decreases. C) I₁ decreases and I₂ increases. D) I₁ increases and I₂ decreases. E) I₁ increases and I₂ increases.

Accepted Answer

As R is decreased, the overall resistance of the circuit decreases, which leads to an increase in the total current, IT. According to Kirchhoff's Law, IT is divided into two branches through the junction. Since the resistance in R1 is fixed, the increase in IT is mainly drawn towards the variable resistor R. Therefore, the current in the branch containing R decreases while the current in the branch containing R1 increases. Hence, I₁ decreases and I₂ increases.

Question 8

Kirchhoff's junction rule is a statement of
A) the law of conservation of momentum.
B) the law of conservation of charge.
C) the law of conservation of energy.
D) the law of conservation of angular momentum.
E) Newton's second law.

Accepted Answer

Kirchhoff's junction rule, also known as Kirchhoff's first law, states that the total incoming current to a junction in a circuit is equal to the total outgoing current from the junction. This is based on the law of conservation of charge, which states that charge cannot be created or destroyed but can only be transferred from one object to another.

Question 9

A capacitor C is connected in series with a resistor R across a battery and an open switch. If a second capacitor of capacitance 2C is connected in parallel with the first one, the time constant of the new RC circuit will be
A) the same as before.
B) twice as large as before.
C) three times a large as before.
D) one-half as large as before.
E) one-fourth as large as before.

Accepted Answer

The answer of A capacitor C is connected in series...

Question 10

An uncharged capacitor is connected in series with a resistor, a dc battery, and an open switch. At time t = 0 s, the switch is closed. Which of the graphs below best describes the potential difference V across the resistor as a function of time t? 
A)

B)

C)

D)

E)

Accepted Answer

The answer of An uncharged capacitor is connected in series...

Question 11

A resistor, an uncharged capacitor, a dc voltage source, and an open switch are all connected in series. The switch is closed at time t = 0 s. Which one of the following is a correct statement about the circuit?
A) The capacitor charges to its maximum value in one time constant.
B) The capacitor charges to its maximum value in two time constants.
C) The potential difference across the resistor is always equal to the potential difference across the capacitor.
D) Current flows through the circuit even after the capacitor is essentially fully charged.
E) Once the capacitor is essentially fully charged, there is no current in the circuit.

Accepted Answer

Once a capacitor is fully charged in a DC circuit, it acts like an open circuit, meaning no current flows through the circuit. This is because the capacitor opposes changes in voltage by storing energy in its electric field, and once fully charged, it maintains the voltage across its plates, preventing further current flow.

Question 12

A resistor, an uncharged capacitor, a dc voltage source, and an open switch are all connected in series. The switch is closed at time t = 0 s. Which one of the following is a correct statement about this circuit?
A) The charge on the capacitor after four time constants is about 98% of the maximum value.
B) The charge on the capacitor after one time constant is 50% of its maximum value.
C) The charge on the capacitor after one time constant is 1/e of its maximum value.
D) The voltage on the capacitor after one time constant is 1/e of the maximum value.
E) The voltage on this capacitor after one time constant is 100% of its maximum value.

Accepted Answer

The answer of A resistor, an uncharged capacitor, a dc...

Question 13

Identical ideal batteries are connected in different arrangements to the same light bulb, as shown in the figure. For which arrangement will the bulb shine the brightest? 
(A)

(B)

(C)

A) A
B) B
C) C

Accepted Answer

The answer of Identical ideal batteries are connected in different...

Question 14

Kirchhoff's loop rule is a statement of
A) the law of conservation of momentum.
B) the law of conservation of charge.
C) the law of conservation of energy.
D) the law of conservation of angular momentum.
E) Newton's second law.

Accepted Answer

Kirchhoff's loop rule, also known as Kirchhoff's voltage law, states that the total voltage around any closed loop in a circuit is zero. This is a statement of the law of conservation of energy, as it implies that all of the energy put into the circuit by the power source is ultimately consumed by the circuit's components.

Question 15

An uncharged capacitor is connected in series with a resistor, a dc battery, and an open switch. At time t = 0 s, the switch is closed. Which of the graphs below best describes the charge Q on the capacitor as a function of time t? 
A)

B)

C)

D)

E)

Accepted Answer

The answer of An uncharged capacitor is connected in series...

Question 16

A 9-V battery is hooked up to two resistors in series. One has a resistance of 5 Ω, and the other has a resistance of 10 Ω. Several locations along the circuit are marked with letters, as shown in the figure. Through which resistor is energy being dissipated at the higher rate? 
A) the 10-Ω resistor
B) the 5-Ω resistor
C) Energy is being dissipated by both resistors at the same rate.

Accepted Answer

The rate at which energy is dissipated by a resistor is proportional to the square of the current passing through it, according to the formula P = I^2R, where P is power, I is current, and R is resistance. Since the resistors are in series, the current passing through each resistor is the same. However, the power dissipated by each resistor is proportional to its resistance. Therefore, the resistor with the higher resistance (the 10-Ω resistor) will dissipate energy at a higher rate than the resistor with the lower resistance (the 5-Ω resistor).

Question 17

For the circuit shown in the figure, write the Kirchhoff current equation for the node labeled A. Notice the directions of the currents!

Accepted Answer

The answer of For the circuit shown in the figure,...

Question 18

A charged capacitor is connected in series with a resistor and an open switch. At time t = 0 s, the switch is closed. Which of the graphs below best describes the charge Q on the capacitor as a function of time t? 
A)

B)

C)

D)

E)

Accepted Answer

The answer of A charged capacitor is connected in series...

Question 19

An uncharged capacitor is connected in series with a resistor, a dc battery, and an open switch. At time t = 0 s, the switch is closed. Which of the graphs below best describes the current I through the resistor as a function of time t? 
A)

B)

C)

D)

E)

Accepted Answer

The answer of An uncharged capacitor is connected in series...

Question 20

A capacitor C is connected in series with a resistor R across a battery and an open switch. If a second capacitor of capacitance 2C is connected in series with the first one, the time constant of the new RC circuit will be
A) the same as before.
B) larger than before.
C) smaller than before.
D) variable.

Accepted Answer

The time constant of an RC circuit is defined as the product of the resistance and capacitance, which is given by τ = RC. When a capacitor of capacitance 2C is connected in series with the first one, the total capacitance becomes 3C. Therefore, the new time constant is given by τ' = R(3C). Since 3C is greater than C, the new time constant is larger than before.

Quiz 23: Circuits

A charged capacitor is connected in series with a resistor and an open switch. At time t = 0 s, the switch is closed. Which of the graphs below best describes the potential difference V across the capacitor as a function of time t?

A charged capacitor is connected in series with a resistor and an open switch. At time t = 0 s, the switch is closed. Which of the graphs below best describes the potential difference V across the resistor as a function of time t?

Identical light bulbs can be attached to identical ideal batteries in three different ways (A, B, orC) , as shown in the figure. The ranking (from lowest to highest) of the total power produced by the battery is

For the circuit shown in the figure, write the Kirchhoff loop equation for the entire outside loop. Notice the directions of the currents!

A charged capacitor is connected in series with a resistor and an open switch. At time t = 0 s, the switch is closed. Which of the graphs below best describes the current I through the resistor as a function of time t?

In the circuit shown in the figure, the resistor R has a variable resistance. As R is decreased, what happens to the currents?

Kirchhoff's junction rule is a statement of

A capacitor C is connected in series with a resistor R across a battery and an open switch. If a second capacitor of capacitance 2C is connected in parallel with the first one, the time constant of the new RC circuit will be

An uncharged capacitor is connected in series with a resistor, a dc battery, and an open switch. At time t = 0 s, the switch is closed. Which of the graphs below best describes the potential difference V across the resistor as a function of time t?

A resistor, an uncharged capacitor, a dc voltage source, and an open switch are all connected in series. The switch is closed at time t = 0 s. Which one of the following is a correct statement about the circuit?

A resistor, an uncharged capacitor, a dc voltage source, and an open switch are all connected in series. The switch is closed at time t = 0 s. Which one of the following is a correct statement about this circuit?

Identical ideal batteries are connected in different arrangements to the same light bulb, as shown in the figure. For which arrangement will the bulb shine the brightest? (A) (B) (C)

Kirchhoff's loop rule is a statement of

An uncharged capacitor is connected in series with a resistor, a dc battery, and an open switch. At time t = 0 s, the switch is closed. Which of the graphs below best describes the charge Q on the capacitor as a function of time t?

A 9-V battery is hooked up to two resistors in series. One has a resistance of 5 Ω, and the other has a resistance of 10 Ω. Several locations along the circuit are marked with letters, as shown in the figure. Through which resistor is energy being dissipated at the higher rate?

For the circuit shown in the figure, write the Kirchhoff current equation for the node labeled A. Notice the directions of the currents!

A charged capacitor is connected in series with a resistor and an open switch. At time t = 0 s, the switch is closed. Which of the graphs below best describes the charge Q on the capacitor as a function of time t?

An uncharged capacitor is connected in series with a resistor, a dc battery, and an open switch. At time t = 0 s, the switch is closed. Which of the graphs below best describes the current I through the resistor as a function of time t?

A capacitor C is connected in series with a resistor R across a battery and an open switch. If a second capacitor of capacitance 2C is connected in series with the first one, the time constant of the new RC circuit will be