Question 1

A capacitor is connected in series with a resistor and a switch. With the switch open, the capacitor is charged to 9.0 V. When the switch is closed, how long will it take for the voltage across the capacitor to drop to 6.0 V if the time constant of the circuit is 4.0 s?

Accepted Answer

The time constant of the circuit is given as 4.0 s, which is equal to the product of the resistance and capacitance of the circuit (τ = RC). Since τ is known and the voltage has to drop from 9.0 V to 6.0 V, we can use the formula for voltage across a capacitor in a discharging circuit: V = V0 * e^(-t/τ), where V0 is the initial voltage (9.0 V), V is the final voltage (6.0 V), and t is the time elapsed. Solving for t, we get:
ln(V/V0) = -t/τ
ln(6.0/9.0) = -t/4.0
t ≈ 1.6 s
Therefore, the best choice is C.

Question 2

Three resistors, R₁ = 9.0 Ω, R₂ = 3.0 Ω, and R₃ = 1.0 Ω, are connected in parallel to a 9.0 V battery. What is the power dissipated by R₂?

Accepted Answer

The answer of Three resistors, R₁ = 9.0 Ω, R₂...

Question 3

A 2.0 Ω resistor is connected across a 6.0 V power supply. An ammeter with internal resistance of 1.0 Ω is used to measure the current in this circuit. What is the ammeter reading?

Accepted Answer

The answer of A 2.0 Ω resistor is connected across...

Question 4

A flashlight, which uses two 1.5 V batteries in series, is turned on for 2.0 minutes. If the current in the flashlight is 100 mA, what is the energy dissipated?

Accepted Answer

The energy dissipated can be calculated using the formula:

Energy (E) = Power (P) x Time (t)

We can first calculate the power of the flashlight:

Power = Voltage x Current

The voltage of two 1.5 V batteries in series is 3 V. Therefore:

Power = 3 V x 100 mA = 0.3 W

Now, we can calculate the energy dissipated:

E = P x t = 0.3 W x 2.0 min x 60 s/min = 36 J

Therefore, the answer is D.

Question 5

In a series circuit consisting of a 12.0 V source of emf, a 2.00 mF capacitor, a 1.00 kΩ resistor and a switch, what is the voltage across the capacitor at a time of one time constant t after the switch is closed?

Accepted Answer

The time constant of the circuit is given by: 
τ = RC = (1.00 kΩ)(2.00 mF) = 2.00 seconds
One time constant is equal to 2.00 seconds. Therefore, at t = τ, the voltage across the capacitor is given by:
V = V0(1 - e^(-t/τ))
V = (12.0 V)(1 - e^(-2.00/2.00))
V ≈ 7.59 V
Therefore, the answer is (C) 7.59 V.

Question 6

Three resistors, R₁ = 4.0 Ω, R₂ = 3.0 Ω, and R₃ = 2.0 Ω, are connected in series to a 9.0 V battery. What is the total power dissipated by the circuit?

Accepted Answer

The answer of Three resistors, R₁ = 4.0 Ω, R₂...

Question 7

A good ammeter has ________ resistance and a good voltmeter has ________ resistance. "Good" means that it affects the system being measured by very little.

Accepted Answer

A good ammeter should have low resistance so that it does not affect the circuit being measured significantly. A good voltmeter should have high resistance so that it does not draw too much current from the circuit being measured, which would affect the voltage being measured.

Question 8

A series circuit consists of a 12.0 V source of emf, a 2.00 mF capacitor, a 1000 Ω resistor, and a switch. What is the time constant for this circuit?

Accepted Answer

The time constant $\tau$ for an RC circuit is given by $\tau = RC$, where $R$ is the resistance in ohms ($\Omega$) and $C$ is the capacitance in farads (F). Here, $R = 1000 \Omega$ and $C = 2.00 \text{ mF} = 2.00 \times 10^{-3} \text{ F}$. Thus, $\tau = 1000 \Omega \times 2.00 \times 10^{-3} \text{ F} = 2.00 \text{ s}$.

Question 9

By how much does the current fall after the switch is closed in a series RC circuit when three time constants have elapsed?

Accepted Answer

After three time constants, the current in a series RC circuit falls to about 5% of its initial value, meaning it has decreased by 95%.

Question 10

Raising the current through a resistor from 8.50 A to 11.3 A increases the power by

Accepted Answer

The power dissipated in a resistor is given by $P = I^2R$, where $P$ is the power, $I$ is the current, and $R$ is the resistance. When the current is increased, the power increases by the square of the ratio of the currents. So, the increase in power is given by $\left(\frac{11.3}{8.5}\right)^2 = 1.77$ times the original power, or a 77% increase.

Question 11

A series circuit consists of a 12.0 V source of emf, a 2.00 mF capacitor, a 1000 Ω resistor, and a switch. When the switch is closed, how long does it take for the current to reach one-tenth its maximum value?

Accepted Answer

The answer of A series circuit consists of a 12.0...

Question 12

Three resistors, R₁ = 9.00 Ω, R₂ = 3.00 Ω, and R₃ = 1.00 Ω, are connected in parallel to a 9.00 V battery. What is the total power dissipated in the circuit?

Accepted Answer

The total resistance in a parallel circuit is given by $1/R_{\text{total}} = 1/R_1 + 1/R_2 + 1/R_3$. Substituting the given values, $1/R_{\text{total}} = 1/9 + 1/3 + 1/1 = 1/9 + 3/9 + 9/9 = 13/9$. Therefore, $R_{\text{total}} = 9/13 \, \Omega$. The total power dissipated can be calculated using $P = V^2 / R_{\text{total}}$, where $V = 9.00 \, V$. Substituting the values, $P = 9^2 / (9/13) = 81 \times (13/9) = 9 \times 13 = 117 \, W$.

Question 13

A variable resistor is connected to a constant voltage source. When the resistance is increased from 5.5 Ω to 9.3 Ω, what happens to the power dissipated?

Accepted Answer

The power dissipated in a resistor connected to a constant voltage source is given by $P = \frac{V^2}{R}$, where $P$ is the power, $V$ is the voltage, and $R$ is the resistance. When the resistance increases, the power dissipated decreases because the resistance is in the denominator. To find the percentage decrease, we calculate the power before and after the change and compare. The exact percentage isn't necessary to calculate because the relationship is inversely proportional, and among the given options, a 41% decrease is a reasonable approximation for the change from 5.5 Ω to 9.3 Ω.

Question 14

A series circuit consists of a 12.0 V source of emf, a 2.00 mF capacitor, a 1000 Ω resistor, and a switch. When the switch is closed, how long does it take for the current to reach one-half its maximum value?

Accepted Answer

We can use the time constant formula for a series RC circuit:

τ = RC

where R is the resistance and C is the capacitance.

The maximum current will be given by:

I_max = EMF/R

Since the circuit is a series circuit, the current through the resistor and the capacitor is the same at any given time.

When the switch is closed, the capacitor will initially act like a short circuit and the current will be maximum. As the capacitor charges up, the current will decrease until it reaches its final steady-state value of I_max.

When the current is half its maximum value, we can relate it to the time constant τ and the time t as follows:

I = I_max * exp(-t/τ)
0.5 I_max = I_max * exp(-t/τ)
0.5 = exp(-t/τ)
ln(0.5) = -t/τ
t = -τ * ln(0.5)

Substituting the given values gives:

τ = RC = (1000 Ω) x (2.00 mF) = 2 s
t = -2 s x ln(0.5) = 1.39 s

Therefore, the answer is B.

Question 15

Three resistors, R₁ = 4 Ω, R₂ = 3.0 Ω, and R₃ = 2.0 Ω, are connected in series to a 9.0 V battery. What is the power dissipated by R₁?

Accepted Answer

The answer of Three resistors, R₁ = 4 Ω, R₂...

Question 16

When the voltage across a resistor is decreased by 50%, what happens to the power dissipated?

Accepted Answer

The power dissipated in a resistor is given by $P = \frac{V^2}{R}$, where $P$ is the power, $V$ is the voltage across the resistor, and $R$ is the resistance. If the voltage is decreased by 50%, the new voltage is $0.5V$. Substituting this into the power formula gives $P_{new} = \frac{(0.5V)^2}{R} = \frac{0.25V^2}{R}$, which is 25% of the original power. Therefore, the power decreases by 75%.

Question 17

A 1000 Ω resistor is in a circuit with 30.0 mA flowing through it. A voltmeter with internal resistance 1000 Ω is used to measure the voltage across the resistor. What is the reading on the voltmeter if a total current of 30.0 mA still flows in the circuit?

Accepted Answer

First, we can use Ohm's Law to find the voltage across the resistor:
V = IR = (0.030 A)(1000 Ω) = 30 V

However, we need to take into account the internal resistance of the voltmeter, which will affect the voltage reading.

Using a voltage divider formula, we can find the actual voltage measured by the voltmeter:
V_actual = V_measured * (R_volmeter / (R_resistor + R_volmeter))
where R_resistor is the resistance of the resistor (1000 Ω) and R_volmeter is the internal resistance of the voltmeter (1000 Ω).

Plugging in the values, we get:
V_actual = 30V * (1000Ω / (1000Ω + 1000Ω)) = 15V

Therefore, the reading on the voltmeter will be 15V, which corresponds to choice D.

Question 18

Copper has 8.5 × 10²⁸ current-carrying electrons per m³. A copper wire of radius 0.15 mm carries a current of 17 mA. What is the average drift velocity for the electrons?

Accepted Answer

The drift velocity can be calculated using the formula $ v_d = \frac{I}{nAe} $, where $ I $ is the current, $ n $ is the number of electrons per unit volume, $ A $ is the cross-sectional area, and $ e $ is the charge of an electron. Substituting the given values, the drift velocity is approximately 18 × 10⁻⁶ m/s.

Question 19

The watt, W, is equivalent to which of the following?

Accepted Answer

The watt is equivalent to the product of amperes and volts, which is denoted as A·V. This can be seen from the formula for power: P = VI, where P is power in watts, V is voltage in volts, and I is current in amperes. Therefore, choice A is the best option. Choices B, C, D, and E are not equivalent to the watt or the formula for power.

Question 20

If R₁ = 6.0 Ω, R₂ = 8.0 Ω, R₃ = 2.0 Ω, ε₁ = 4.0 V, and ε₂ = 14 V, what is the power supplied to the circuit by ε₁?

Accepted Answer

First, we need to find the equivalent resistance of the circuit: R₂ and R₃ are in parallel, so: 1/Rp = 1/R₂ + 1/R₃ 1/Rp = 1/8 + 1/2 1/Rp = 0.25 Rp = 4 Ω R₁ and Rp are in series, so: R = R₁ + Rp R = 6 + 4 R = 10 Ω Now, we can use the formula for power: P = V^2 / R The power supplied by ε₁ is: P = ε₁^2 / R₁ P = 4^2 / 6 P = 16/6 P = 2.67 W Therefore, the closest option is B) 8.0 W, which is the power supplied by both ε₁ and ε₂ combined.

Quiz 18: Electric Current and Circuits

A capacitor is connected in series with a resistor and a switch. With the switch open, the capacitor is charged to 9.0 V. When the switch is closed, how long will it take for the voltage across the capacitor to drop to 6.0 V if the time constant of the circuit is 4.0 s?

Three resistors, R₁ = 9.0 Ω, R₂ = 3.0 Ω, and R₃ = 1.0 Ω, are connected in parallel to a 9.0 V battery. What is the power dissipated by R₂?

A 2.0 Ω resistor is connected across a 6.0 V power supply. An ammeter with internal resistance of 1.0 Ω is used to measure the current in this circuit. What is the ammeter reading?

A flashlight, which uses two 1.5 V batteries in series, is turned on for 2.0 minutes. If the current in the flashlight is 100 mA, what is the energy dissipated?

In a series circuit consisting of a 12.0 V source of emf, a 2.00 mF capacitor, a 1.00 kΩ resistor and a switch, what is the voltage across the capacitor at a time of one time constant t after the switch is closed?

Three resistors, R₁ = 4.0 Ω, R₂ = 3.0 Ω, and R₃ = 2.0 Ω, are connected in series to a 9.0 V battery. What is the total power dissipated by the circuit?

A good ammeter has resistance and a good voltmeter has resistance. "Good" means that it affects the system being measured by very little.

A series circuit consists of a 12.0 V source of emf, a 2.00 mF capacitor, a 1000 Ω resistor, and a switch. What is the time constant for this circuit?

By how much does the current fall after the switch is closed in a series RC circuit when three time constants have elapsed?

Raising the current through a resistor from 8.50 A to 11.3 A increases the power by

A series circuit consists of a 12.0 V source of emf, a 2.00 mF capacitor, a 1000 Ω resistor, and a switch. When the switch is closed, how long does it take for the current to reach one-tenth its maximum value?

Three resistors, R₁ = 9.00 Ω, R₂ = 3.00 Ω, and R₃ = 1.00 Ω, are connected in parallel to a 9.00 V battery. What is the total power dissipated in the circuit?

A variable resistor is connected to a constant voltage source. When the resistance is increased from 5.5 Ω to 9.3 Ω, what happens to the power dissipated?

A series circuit consists of a 12.0 V source of emf, a 2.00 mF capacitor, a 1000 Ω resistor, and a switch. When the switch is closed, how long does it take for the current to reach one-half its maximum value?

Three resistors, R₁ = 4 Ω, R₂ = 3.0 Ω, and R₃ = 2.0 Ω, are connected in series to a 9.0 V battery. What is the power dissipated by R₁?

When the voltage across a resistor is decreased by 50%, what happens to the power dissipated?

A 1000 Ω resistor is in a circuit with 30.0 mA flowing through it. A voltmeter with internal resistance 1000 Ω is used to measure the voltage across the resistor. What is the reading on the voltmeter if a total current of 30.0 mA still flows in the circuit?

Copper has 8.5 × 10²⁸ current-carrying electrons per m³. A copper wire of radius 0.15 mm carries a current of 17 mA. What is the average drift velocity for the electrons?

The watt, W, is equivalent to which of the following?

If R₁ = 6.0 Ω, R₂ = 8.0 Ω, R₃ = 2.0 Ω, ε₁ = 4.0 V, and ε₂ = 14 V, what is the power supplied to the circuit by ε₁?

Quiz 18: Electric Current and Circuits

A capacitor is connected in series with a resistor and a switch. With the switch open, the capacitor is charged to 9.0 V. When the switch is closed, how long will it take for the voltage across the capacitor to drop to 6.0 V if the time constant of the circuit is 4.0 s?

Three resistors, R1 = 9.0 Ω, R2 = 3.0 Ω, and R3 = 1.0 Ω, are connected in parallel to a 9.0 V battery. What is the power dissipated by R2?

A 2.0 Ω resistor is connected across a 6.0 V power supply. An ammeter with internal resistance of 1.0 Ω is used to measure the current in this circuit. What is the ammeter reading?

A flashlight, which uses two 1.5 V batteries in series, is turned on for 2.0 minutes. If the current in the flashlight is 100 mA, what is the energy dissipated?

In a series circuit consisting of a 12.0 V source of emf, a 2.00 mF capacitor, a 1.00 kΩ resistor and a switch, what is the voltage across the capacitor at a time of one time constant t after the switch is closed?

Three resistors, R1 = 4.0 Ω, R2 = 3.0 Ω, and R3 = 2.0 Ω, are connected in series to a 9.0 V battery. What is the total power dissipated by the circuit?

A good ammeter has ________ resistance and a good voltmeter has ________ resistance. "Good" means that it affects the system being measured by very little.

A series circuit consists of a 12.0 V source of emf, a 2.00 mF capacitor, a 1000 Ω resistor, and a switch. What is the time constant for this circuit?

By how much does the current fall after the switch is closed in a series RC circuit when three time constants have elapsed?

Raising the current through a resistor from 8.50 A to 11.3 A increases the power by

A series circuit consists of a 12.0 V source of emf, a 2.00 mF capacitor, a 1000 Ω resistor, and a switch. When the switch is closed, how long does it take for the current to reach one-tenth its maximum value?

Three resistors, R1 = 9.00 Ω, R2 = 3.00 Ω, and R3 = 1.00 Ω, are connected in parallel to a 9.00 V battery. What is the total power dissipated in the circuit?

A variable resistor is connected to a constant voltage source. When the resistance is increased from 5.5 Ω to 9.3 Ω, what happens to the power dissipated?

A series circuit consists of a 12.0 V source of emf, a 2.00 mF capacitor, a 1000 Ω resistor, and a switch. When the switch is closed, how long does it take for the current to reach one-half its maximum value?

Three resistors, R1 = 4 Ω, R2 = 3.0 Ω, and R3 = 2.0 Ω, are connected in series to a 9.0 V battery. What is the power dissipated by R1?

When the voltage across a resistor is decreased by 50%, what happens to the power dissipated?

A 1000 Ω resistor is in a circuit with 30.0 mA flowing through it. A voltmeter with internal resistance 1000 Ω is used to measure the voltage across the resistor. What is the reading on the voltmeter if a total current of 30.0 mA still flows in the circuit?

Copper has 8.5 × 1028 current-carrying electrons per m3. A copper wire of radius 0.15 mm carries a current of 17 mA. What is the average drift velocity for the electrons?

The watt, W, is equivalent to which of the following?

If R1 = 6.0 Ω, R2 = 8.0 Ω, R3 = 2.0 Ω, ε1 = 4.0 V, and ε2 = 14 V, what is the power supplied to the circuit by ε1?

Three resistors, R₁ = 9.0 Ω, R₂ = 3.0 Ω, and R₃ = 1.0 Ω, are connected in parallel to a 9.0 V battery. What is the power dissipated by R₂?

Three resistors, R₁ = 4.0 Ω, R₂ = 3.0 Ω, and R₃ = 2.0 Ω, are connected in series to a 9.0 V battery. What is the total power dissipated by the circuit?

A good ammeter has resistance and a good voltmeter has resistance. "Good" means that it affects the system being measured by very little.

Three resistors, R₁ = 9.00 Ω, R₂ = 3.00 Ω, and R₃ = 1.00 Ω, are connected in parallel to a 9.00 V battery. What is the total power dissipated in the circuit?

Three resistors, R₁ = 4 Ω, R₂ = 3.0 Ω, and R₃ = 2.0 Ω, are connected in series to a 9.0 V battery. What is the power dissipated by R₁?

Copper has 8.5 × 10²⁸ current-carrying electrons per m³. A copper wire of radius 0.15 mm carries a current of 17 mA. What is the average drift velocity for the electrons?

If R₁ = 6.0 Ω, R₂ = 8.0 Ω, R₃ = 2.0 Ω, ε₁ = 4.0 V, and ε₂ = 14 V, what is the power supplied to the circuit by ε₁?