Question 1

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 time constant of an RC circuit is given by τ = R*C. When a second capacitor of capacitance 2C is connected in parallel with the first capacitor C, the total capacitance becomes C + 2C = 3C. Therefore, the new time constant is τ' = R*(3C), which is three times the original time constant τ = R*C.

Question 2

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 given by the product of resistance and capacitance. Therefore, for the first circuit, the time constant is RC. When a second capacitor of capacitance 2C is added in series, the effective capacitance of the circuit becomes 1/((1/C)+(1/2C)) = 2/3C. Therefore, the new time constant becomes R(2/3C), which is smaller than the original time constant RC. Hence, the correct choice is C.

Question 3

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 answer of A 9-V battery is hooked up to...

Question 4

A electric heater that draws 13.5 A of dc current has been left on for 10 min.How many electrons that have passed through the heater during that time? (e = 1.60 × 10^-19C) A)1.5 × 10²² B)5.1 × 10²² C)1.8 × 10³ D)8.1 × 10³ E)1.0 × 10²³

Accepted Answer

First, we need to calculate the total charge that passed through the heater:

Q = I*t
Q = 13.5 A * 10 min * 60 s/min
Q = 8100 C

Then, we can use the definition of electric charge to find the number of electrons:

Q = n*e
n = Q/e
n = 8100 C / (1.60 × 10^-19 C/e)
n = 5.0625 × 10^22 electrons

Rounding to two significant figures, we get:

n = 5.1 × 10^22 electrons, which corresponds to answer choice B.

Question 5

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

The resistance of a wire is directly proportional to its length. If the wire is cut in half, the resistance of each half will be half of the original resistance. When the two halves are connected in parallel, the total resistance will be half of the resistance of one half. Therefore, the current will be doubled.

Question 6

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 amount of electric charge entering a junction in a circuit must equal the total amount of electric charge leaving the junction. This is a statement of the law of conservation of charge.

Question 7

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

In case A, the battery is connected to a single bulb, so the power produced is P. In case B, the battery is connected to two bulbs in parallel, so the power produced is 2P. In case C, the battery is connected to two bulbs in series, so the power produced is P/2. Therefore, the ranking from lowest to highest is A, B, C.

Question 8

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

After four time constants, the charge on the capacitor is approximately 98% of its maximum value, as the capacitor charges exponentially towards its maximum charge.

Question 9

What current is flowing in a wire if 0.67 C of charge pass a point in the wire in 0.30 s?
A)2.2 A
B)0.67 A
C)0.30 A
D)0.20 A

Accepted Answer

The current can be calculated using the formula I = Q/t, where I is the current in amperes, Q is the charge in coulombs, and t is the time in seconds. Substituting the given values, I = 0.67 C / 0.30 s = 2.23 A, which rounds to 2.2 A.

Question 10

A charge of 12 C passes through an electroplating apparatus in 2.0 min.What is the average current in the apparatus?
A)0.10 A
B)0.60 A
C)1.0 A
D)6.0 A

Accepted Answer

Average current = Charge / Time = 12 C / 2.0 min = 6.0 A

Question 11

A current of 5.0 A flows through an electrical device for 10 seconds.How many electrons flow through this device during this time? (e = 1.60 × 10^-19C) A)0.20 B)20 C)2.0 D)3.1 × E)31 ×

Accepted Answer

The answer of A current of 5.0 A flows through...

Question 12

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 second law, is a statement of the law of conservation of energy in electrical circuits. It states that the sum of the potential differences around any closed loop in a circuit must be equal to zero. This is based on the principle that energy is neither created nor destroyed, only transferred or converted from one form to another.

Question 13

What current is flowing in a resistor if 4.0 × 10¹⁶ electrons pass a point in the resistor in 0.50 s? (e = 1.60 × 10^-19C) A)0.013 A B)0.31 A C)6.3 A D)78 A

Accepted Answer

The current can be calculated using the formula $I = \frac{q}{t}$, where $q$ is the charge and $t$ is the time. Given $4.0 \times 10^{16}$ electrons, each with a charge of $1.60 \times 10^{-19} C$, the total charge $q = 4.0 \times 10^{16} \times 1.60 \times 10^{-19} C = 6.4 \times 10^{-3} C$. With $t = 0.50 s$, the current $I = \frac{6.4 \times 10^{-3} C}{0.50 s} = 0.0128 A$, which rounds to $0.013 A$.

Question 14

If 3.0 × 10¹⁵ electrons flow through a section of a wire of diameter 2.0 mm in 4.0 s,what is the current in the wire? (e = 1.60 × 10^-19C) A)0.12 mA B)0.24 mA C)7.5 × 10⁷ A D)7.5 × 10¹⁴ A

Accepted Answer

The current I can be calculated using the formula I = Q/t, where Q is the charge and t is the time. Given that 3.0 × 10^15 electrons flow through the wire in 4.0 s, and each electron has a charge of 1.60 × 10^-19 C, the total charge Q = 3.0 × 10^15 electrons × 1.60 × 10^-19 C/electron = 4.8 × 10^-4 C. Therefore, the current I = Q/t = 4.8 × 10^-4 C / 4.0 s = 1.2 × 10^-4 C/s = 0.12 mA.

Question 15

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 16

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 total resistance of the circuit decreases. According to Ohm's Law, the current flowing through a circuit is directly proportional to the voltage and inversely proportional to the resistance. Therefore, as the resistance decreases, the current increases. Since R is in series with I₁, the current through this branch, I₁, decreases. On the other hand, I₂ is in parallel with R, so the current through this branch, I₂, increases. Therefore, the correct choice is C.

Question 17

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)A
B)B
C)C

Accepted Answer

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

Question 18

How much charge must pass by a point in a wire in 10 s for the current in the wire to be 0.50 A?
A)20 C
B)2.0 C
C)5.0 C
D)0.050 C

Accepted Answer

The current (I) is the charge (Q) passing through a point per unit time (t). Using the formula I = Q/t, we can solve for Q: Q = I * t = 0.50 A * 10 s = 5.0 C.

Question 19

In an electroplating process,it is desired to deposit 40 mg of silver on a metal part by using a current of 2.0 A.How long must the current be allowed to run to deposit this much silver? The silver ions are singly charged,and the atomic mass of silver is 108 g/mol.(e = 1.60 × 10^-19 C,N_A = 6.02 × 10²³ atoms/mol) A)16 s B)18 s C)20 s D)22 s

Accepted Answer

First, we need to calculate the number of moles of silver required to deposit 40 mg:

1 mol of Ag = 108 g

1 mol of Ag = 6.02 × 10^23 atoms

40 mg of Ag = 40/108 × 6.02 × 10^23 atoms

40 mg of Ag = 2.23 × 10^21 atoms

Now, we can calculate the amount of charge required to deposit 2.23 × 10^21 silver ions:

1 Ag ion = 1 e⁻ (since it is singly charged)

2.23 × 10^21 Ag ions = 2.23 × 10^21 e⁻

Q = ne

Q = (2.23 × 10^21)(1.60 × 10^-19)

Q = 3.57 × 10² C

Finally, we can use the formula for electric charge:

Q = It

where Q is the charge, I is the current, and t is the time.

Solving for t:

t = Q/I

t = 3.57 × 10² / 2.0

t = 178.5 s

Rounding off to the nearest second, we get:

t = 18 s

Therefore, the correct answer is B) 18 s.

Question 20

A total of 2.0 × 10¹³ electrons pass a given point in a wire in 15 s.What is the current in the wire? (e = 1.60 × 10^-19C) A)1.3 mA B)1.3 A C)0.21 μA D)3.2 μA

Accepted Answer

To find the current, we need to use the formula:

I = Q/t

where I is the current, Q is the charge passing through the point, and t is the time for which the charge flows.

First, we need to find the total charge passing through the point:

Q = ne

where n is the number of electrons and e is the charge on an electron.

Q = (2.0 × 10^19)(1.60 × 10^-19) = 3.2 × 10^-6 C

Now, we can find the current:

I = Q/t = (3.2 × 10^-6 C)/(15 s) = 0.21 μA

Therefore, the best choice is C, 0.21 μA.

Quiz 21: Electric Current and Direct-Current Circuits

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 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 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 electric heater that draws 13.5 A of dc current has been left on for 10 min.How many electrons that have passed through the heater during that time? (e = 1.60 × 10^-19C)

Kirchhoff's junction rule is a statement of

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 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?

What current is flowing in a wire if 0.67 C of charge pass a point in the wire in 0.30 s?

A charge of 12 C passes through an electroplating apparatus in 2.0 min.What is the average current in the apparatus?

A current of 5.0 A flows through an electrical device for 10 seconds.How many electrons flow through this device during this time? (e = 1.60 × 10^-19C)

Kirchhoff's loop rule is a statement of

What current is flowing in a resistor if 4.0 × 10¹⁶ electrons pass a point in the resistor in 0.50 s? (e = 1.60 × 10^-19C)

If 3.0 × 10¹⁵ electrons flow through a section of a wire of diameter 2.0 mm in 4.0 s,what is the current in the wire? (e = 1.60 × 10^-19C)

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?

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

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?

How much charge must pass by a point in a wire in 10 s for the current in the wire to be 0.50 A?

A total of 2.0 × 10¹³ electrons pass a given point in a wire in 15 s.What is the current in the wire? (e = 1.60 × 10^-19C)