Question 1

A 120-V rms signal at 60.0 Hz is applied across a 30.0-mH inductor and a 100-Ω resistor. What is the rms value of the voltage across the inductor?
A) 0.700 V
B) 119 V
C) 100 V
D) 13.5 V
E) 120 V

Accepted Answer

The impedance of the circuit can be found using the formula:

Z = √(R^2 + XL^2)

where R is the resistance, XL is the inductive reactance, and Z is the impedance.

XL can be found using the formula:

XL = 2πfL

where f is the frequency and L is the inductance.

Substituting the given values, we get:

XL = 2π(60)(30×10^-3) = 11.3 Ω

Z = √(100^2 + 11.3^2) = 100.6 Ω

The rms current in the circuit can be found using Ohm's law:

I = Vrms/Z = (120/√2)/100.6 = 1.19 A

The voltage across the inductor can then be found using the formula:

VL = XLI = 11.3 × 1.19 = 13.5 V

Therefore, the answer is D.

Question 2

A 120-V rms voltage at 60.0 Hz is applied across an inductor, a capacitor, and a resistor in series. If the rms value of the current in this circuit is 0.600 A, what is the impedance of this circuit?
A) 200 Ω
B) 141 Ω
C) 20 4 Ω
D) 120 Ω
E) 100 Ω

Accepted Answer

The impedance of a series circuit is given by the formula Z = sqrt(R^2 + (XL - XC)^2), where R is the resistance, XL is the inductive reactance, and XC is the capacitive reactance. In this problem, we are given that the rms voltage is 120 V, the rms current is 0.600 A, and the frequency is 60.0 Hz. We can use Ohm's law to find the resistance: R = V/I = 120 V / 0.600 A = 200 ohms. We can also use the formulas for inductive reactance and capacitive reactance to find XL and XC: XL = 2*pi*f*L and XC = 1/(2*pi*f*C). However, we are not given the values of L and C, so we cannot calculate XL and XC. Therefore, we cannot calculate the impedance of the circuit.

Question 3

What inductance must be put in series with a 200-Ω resistor at 4000 Hz to have a total impedance of 240 Ω?
A) 3.28 mH
B) 4.28 mH
C) 5.28 mH
D) 6.28 mH
E) 12 mH

Accepted Answer

The answer of What inductance must be put in series...

Question 4

An ac signal at a certain frequency is applied across a 40-mH inductor and a 100-Ω resistor. If the power factor of this circuit is 0.40, what is the value of the frequency?
A) 160 Hz
B) 200 Hz
C) 410 Hz
D) 600 Hz
E) 910 Hz

Accepted Answer

The answer of An ac signal at a certain frequency...

Question 5

A certain ac signal at 1000 Hz is applied across an inductor and a 100-Ω resistor. If the power factor of the circuit is 0.400, what is the impedance of this circuit?
A) 150 Ω
B) 200 Ω
C) 250 Ω
D) 100 Ω
E) 300 Ω

Accepted Answer

The power factor of the circuit is given by the ratio of the resistance to the total impedance of the circuit:

cos θ = R/Z

where θ is the phase angle between the current and the voltage.

Given that the power factor is 0.4, we can write:

0.4 = 100/ Z 
Z = 100/0.4 = 250 Ω

Therefore, the impedance of the circuit is 250 Ω.

Question 6

A 20.0-mH inductor is connected in series with a 100-Ω resistor at 1000 Hz. What is the phase angle of this circuit?
A) 90.0°
B) 51.5°
C) 38.5°
D) 0°
E) 45°

Accepted Answer

The phase angle is given by:$$\phi = \arctan\left(\frac{2\pi f L}{R}ight)$$$$\phi = \arctan\left(\frac{2\pi (1000 	ext{ Hz})(20.0 	ext{ mH})}{100 \Omega}ight)$$$$\phi = 51.5°$$

Question 7

What resistance must be put in series with a 30-mH inductor at 4000 Hz to have a total impedance of 8.0 × 10⁴ Ω? A) 30 × 10⁴ Ω B) 5.0 × 10⁴ Ω C) 6.0 × 10⁴ Ω D) 7.0 × 10⁴ Ω E) 8.0 × 10⁴ Ω

Accepted Answer

The answer of What resistance must be put in series...

Question 8

The phase angle of an RLC series circuit with an inductive reactance of 200 Ω, a resistor of 200 Ω and a certain capacitor at 1000 Hz is 40.0°. What is the value of the capacitance in this circuit?
A) 1.95 μF
B) 2.95 μF
C) 3.95 μF
D) 4.95 μF
E) 5.95 μF

Accepted Answer

The answer of The phase angle of an RLC series...

Question 9

A 120-V rms voltage at 60.0 Hz is applied across an inductor, capacitor and a 100-Ω resistor in series. If the maximum value of the current in this circuit is 1.60 A, what is the rms value of the current in this circuit?
A) 1.13 A
B) 2.26 A
C) 1.82 A
D) 1.60 A
E) 2.66 A

Accepted Answer

The answer of A 120-V rms voltage at 60.0 Hz...

Question 10

The phase angle of a series RL circuit with a 100.0-Ω resistor and a 20.00-mH inductor is 70.00°. What is the inductive reactance of this circuit?
A) 100.0 Ω
B) 150.0 Ω
C) 200.0 Ω
D) 174.7 Ω
E) 274.7 Ω

Accepted Answer

The answer of The phase angle of a series RL...

Question 11

A 25.0-mH inductor, a 2.00-μF capacitor, and a certain resistor are connected in series across an ac voltage source at 1000 Hz. If the impedance of this circuit is 200 Ω, what is the value of the resistor?
A) 100 Ω
B) 184 Ω
C) 552 Ω
D) 579 Ω
E) 200 Ω

Accepted Answer

At resonance, the reactance of the inductor and the capacitor will cancel each other out, leaving only the resistance in the circuit. We can use the formula for impedance of a series RLC circuit at resonance to find the value of the resistor:

Z = R

Z = √(R^2 + (XL - XC)^2)  (at resonance, XL = XC)

Z = √(R^2 + 0) = R

200 Ω = R

Therefore, the value of the resistor is 200 Ω.

Question 12

The phase angle of an RLC series circuit with a capacitive reactance of 40 Ω, a resistor of 100 Ω and a certain inductor at 1000 Hz is 40.0°. What is the value of the inductance in this circuit?
A) 11.8 mH
B) 124 mH
C) 212 mH
D) 61.9 mH
E) 19.7 mH

Accepted Answer

The answer of The phase angle of an RLC series...

Question 13

The phase angle in a series RL circuit at 1000 Hz with a 200-Ω resistor and a certain inductor is 40.0°. What is the value of the inductance in this circuit?
A) 83.9 mH
B) 73.9 mH
C) 26.7 mH
D) 36.7 mH
E) 57.9 mH

Accepted Answer

The answer of The phase angle in a series RL...

Question 14

A 200-Ω resistor, a 25-mH inductor, and a capacitor are connected in series across an ac voltage source at 1000 Hz. If the impedance of this circuit is 240 Ω, what is the value of the capacitor?
A) 5.5 μF
B) 3.2 μF
C) 4.2 μF
D) 6.5 μF
E) 7.5 μF

Accepted Answer

The answer of A 200-Ω resistor, a 25-mH inductor, and...

Question 15

A 50.0-mH inductor is connected in series with a 2500-Ω resistor. What is the phase angle at 3000 Hz?
A) 20.7°
B) - 20.7°
C) -75.9°
D) 75.9°
E) 90.0°

Accepted Answer

The phase angle is given by:$$\phi = \arctan\left(\frac{XL}{R}\right)$$where:* XL is the inductive reactance* R is the resistanceAt 3000 Hz, the inductive reactance is:$$XL = 2\pi f L = 2\pi (3000 Hz) (50.0 mH) = 942.5 \Omega$$Therefore, the phase angle is:$$\phi = \arctan\left(\frac{942.5 \Omega}{2500 \Omega}\right) = 20.7°$$

Question 16

A 200-Ω resistor, 40.0-mH inductor and a 2.00-μF capacitor are connected in series with a 120-V rms source at 1000 Hz. What is the phase angle of this circuit?
A) 49.3°
B) 90.0°
C) 40.7°
D) 0°
E) 45.0°

Accepted Answer

We can use the impedance triangle to find the impedance of the circuit:

- The resistance has an impedance of R = 200 Ω. 
- The inductive reactance has an impedance of XL = ωL = 2πfL = 251.3 Ω (where f=1000 Hz). 
- The capacitive reactance has an impedance of Xc = 1/(ωC) = 398.1 Ω.

Using the Pythagorean theorem, we can find the total impedance:

Z = sqrt(R^2 + (XL - Xc)^2) = 294.1 Ω

The phase angle is given by:

θ = arctan((XL - Xc)/R) = 40.7°

Therefore, the answer is C.

Question 17

The phase angle of a series RL circuit with a 20.0-mH inductor and a certain resistor at 1000 Hz is 20.0°. What is the value of the resistance in this circuit?
A) 145 Ω
B) 100 Ω
C) 245 Ω
D) 200 Ω
E) 345 Ω

Accepted Answer

The answer of The phase angle of a series RL...

Question 18

The phase angle of an RLC series circuit with an inductive reactance of 200 Ω and a capacitive reactance of 100 Ω is 40.0°. What is the value of the resistor in this circuit?
A) 100 Ω
B) 119 Ω
C) 156 Ω
D) 200 Ω
E) 265 Ω

Accepted Answer

The phase angle of an RLC series circuit with an inductive reactance (XL) and a capacitive reactance (XC) can be calculated using the formula:

Φ = arctan((XL - XC)/R)

We know Φ = 40.0°, XL = 200 Ω, and XC = 100 Ω.

Substituting these values into the formula and solving for R, we get:

R = (XL - XC)/tan(Φ) = (200 - 100)/tan(40.0°) ≈ 118.95 ≈ 119 Ω

Therefore, the best choice is B, 119 Ω.

Question 19

A 200-Ω resistor, a 40.0-mH inductor and a 2.00-μF capacitor are connected in series with a 120-V rms source at 1000 Hz. What is the impedance of this circuit?
A) 164 Ω
B) 120 Ω
C) 264 Ω
D) 200 Ω
E) 364 Ω

Accepted Answer

The impedance of the series RLC circuit can be calculated using the formula:

Z = sqrt((R^2 + (XL - XC)^2))

where R is the resistance, XL is the inductive reactance, and XC is the capacitive reactance.

We can calculate XL and XC as follows:

XL = 2πfL = 2π(1000)(0.04) = 25.13 Ω

XC = 1/(2πfC) = 1/(2π(1000)(2X10^-6)) = 79.58 Ω

Plugging in the values, we get:

Z = sqrt((200^2 + (25.13 - 79.58)^2)) = 264 Ω

Therefore, the impedance of the circuit is 264 Ω.

Question 20

A certain ac signal at 60 Hz is applied across a 40-mH inductor and a 200-Ω resistor. What is the power factor of this circuit?
A) 0.249
B) 0.497
C) 0.697
D) 0.997
E) None of the other answers is correct.

Accepted Answer

The power factor is the cosine of the phase angle, which is determined by the impedance of the circuit. The inductive reactance (X_L) is 2πfL = 2π(60)(0.04) = 15.08 Ω. The impedance (Z) is √(R^2 + X_L^2) = √(200^2 + 15.08^2) ≈ 200.57 Ω. The power factor is R/Z = 200/200.57 ≈ 0.997.

Quiz 24: Alternating-Current Circuits

A 120-V rms signal at 60.0 Hz is applied across a 30.0-mH inductor and a 100-Ω resistor. What is the rms value of the voltage across the inductor?

A 120-V rms voltage at 60.0 Hz is applied across an inductor, a capacitor, and a resistor in series. If the rms value of the current in this circuit is 0.600 A, what is the impedance of this circuit?

What inductance must be put in series with a 200-Ω resistor at 4000 Hz to have a total impedance of 240 Ω?

An ac signal at a certain frequency is applied across a 40-mH inductor and a 100-Ω resistor. If the power factor of this circuit is 0.40, what is the value of the frequency?

A certain ac signal at 1000 Hz is applied across an inductor and a 100-Ω resistor. If the power factor of the circuit is 0.400, what is the impedance of this circuit?

A 20.0-mH inductor is connected in series with a 100-Ω resistor at 1000 Hz. What is the phase angle of this circuit?

What resistance must be put in series with a 30-mH inductor at 4000 Hz to have a total impedance of 8.0 × 104 Ω?

The phase angle of an RLC series circuit with an inductive reactance of 200 Ω, a resistor of 200 Ω and a certain capacitor at 1000 Hz is 40.0°. What is the value of the capacitance in this circuit?

A 120-V rms voltage at 60.0 Hz is applied across an inductor, capacitor and a 100-Ω resistor in series. If the maximum value of the current in this circuit is 1.60 A, what is the rms value of the current in this circuit?

The phase angle of a series RL circuit with a 100.0-Ω resistor and a 20.00-mH inductor is 70.00°. What is the inductive reactance of this circuit?

A 25.0-mH inductor, a 2.00-μF capacitor, and a certain resistor are connected in series across an ac voltage source at 1000 Hz. If the impedance of this circuit is 200 Ω, what is the value of the resistor?

The phase angle of an RLC series circuit with a capacitive reactance of 40 Ω, a resistor of 100 Ω and a certain inductor at 1000 Hz is 40.0°. What is the value of the inductance in this circuit?

The phase angle in a series RL circuit at 1000 Hz with a 200-Ω resistor and a certain inductor is 40.0°. What is the value of the inductance in this circuit?

A 200-Ω resistor, a 25-mH inductor, and a capacitor are connected in series across an ac voltage source at 1000 Hz. If the impedance of this circuit is 240 Ω, what is the value of the capacitor?

A 50.0-mH inductor is connected in series with a 2500-Ω resistor. What is the phase angle at 3000 Hz?

A 200-Ω resistor, 40.0-mH inductor and a 2.00-μF capacitor are connected in series with a 120-V rms source at 1000 Hz. What is the phase angle of this circuit?

The phase angle of a series RL circuit with a 20.0-mH inductor and a certain resistor at 1000 Hz is 20.0°. What is the value of the resistance in this circuit?

The phase angle of an RLC series circuit with an inductive reactance of 200 Ω and a capacitive reactance of 100 Ω is 40.0°. What is the value of the resistor in this circuit?

A 200-Ω resistor, a 40.0-mH inductor and a 2.00-μF capacitor are connected in series with a 120-V rms source at 1000 Hz. What is the impedance of this circuit?

A certain ac signal at 60 Hz is applied across a 40-mH inductor and a 200-Ω resistor. What is the power factor of this circuit?

What resistance must be put in series with a 30-mH inductor at 4000 Hz to have a total impedance of 8.0 × 10⁴ Ω?