Question 1

What is the effective (rms)current value for an AC current with an amplitude of 15.4 A?

Accepted Answer

The effective (rms) current value for an AC current with an amplitude of 15.4 A can be calculated as:
Irms = Iamp/√2 = 15.4/√2 = 10.9 A (rounded to one decimal place)
Therefore, the best choice is C.

Question 2

When a 47-μF capacitor is attached to an AC source,its capacitive reactance is 42.0 Ω.If instead a 150-μF capacitor is attached to the same source,what will be its capacitive reactance?

Accepted Answer

The capacitive reactance $X_C$ of a capacitor in an AC circuit is given by the formula $X_C = \frac{1}{2\pi fC}$, where $f$ is the frequency of the AC source and $C$ is the capacitance of the capacitor. Since the frequency $f$ and $2\pi$ are constants for the same AC source, the capacitive reactance is inversely proportional to the capacitance $C$. Therefore, if the capacitance increases, the capacitive reactance decreases. Given that the 47-μF capacitor has a reactance of 42.0 Ω, when the capacitance is increased to 150-μF, the reactance will decrease. To find the new reactance, use the ratio of the capacitances:$$\frac{X_{C1}}{X_{C2}} = \frac{C_2}{C_1}$$$$\frac{42.0\, \Omega}{X_{C2}} = \frac{150\, \mu F}{47\, \mu F}$$Solving for $X_{C2}$ gives:$$X_{C2} = \frac{42.0\, \Omega \times 47\, \mu F}{150\, \mu F} \approx 13\, \Omega$$Therefore, the capacitive reactance of the 150-μF capacitor is approximately 13 Ω.

Question 3

An AC voltage source,with a peak output of 114 V,is connected to a 40.0-Ω resistor.What is the effective (or rms)current in the circuit?

Accepted Answer

The effective (or rms) current in an AC circuit is given by the peak current divided by the square root of 2. In this case, the peak current is 114 V / 40.0 Ω = 2.85 A, so the effective current is 2.85 A / √2 = 2.02 A.

Question 4

In a capacitor in an AC circuit,the voltage:

Accepted Answer

In a capacitor, the current leads the voltage by 90°, which means that the voltage lags the current by 90°. This is true for all frequencies, unlike choice C which suggests that the phase relationship depends on frequency. Choice D is incorrect as 70.7% phase shift is only true for a specific type of circuit (RC circuit) and not universally applicable.

Question 5

The frequency in an AC series circuit is quadrupled.By what factor does this change the capacitive reactance?

Accepted Answer

The capacitive reactance (Xc) in an AC circuit is given by the formula Xc = 1/(2πfC), where f is the frequency and C is the capacitance. If the frequency is quadrupled, the new capacitive reactance becomes 1/(4*2πfC) = 1/4 * 1/(2πfC), which means the capacitive reactance is reduced to one-fourth of its original value.

Question 6

A 400-Ω resistor and a capacitor are connected in parallel across a 300-Hz source.If the amplitude of the current in the resistor is equal to that in the capacitor,what is the value of the capacitance?

Accepted Answer

The amplitude of the current in the resistor (I_R) is given by I_R = V/R, and the amplitude of the current in the capacitor (I_C) is given by I_C = VωC, where V is the voltage across the resistor and capacitor, ω is the angular frequency (ω = 2πf, with f being the frequency), and C is the capacitance. Given that I_R = I_C, we can set the two expressions equal to each other and solve for C: V/R = VωC => C = 1/(Rω) = 1/(400*2π*300) ≈ 1.33 μF.

Question 7

The rms current is equal to the direct current that:

Accepted Answer

The root mean square (rms) current is defined as the direct current that dissipates the same amount of energy in a resistor as an alternating current (AC) does over one cycle. This is because the power dissipated by a resistor (P = I^2R for DC, and P = I_rms^2R for AC) is directly proportional to the square of the current through the resistor.

Question 8

The current in an inductor connected to an AC voltage source lags the voltage.This lag is caused by the:

Accepted Answer

The lag or phase shift between the voltage and current in an inductor is caused by the production of a back electromotive force (EMF) in the coil as the current flows through it. This back EMF opposes the applied voltage and causes the current to lag behind the voltage. The larger the inductance, the greater the lag or phase shift. Therefore, choice A, back EMF in the coil, is the best answer.

Question 9

In an AC series circuit,the current in a pure resistor differs in phase with the applied voltage by what angle?

Accepted Answer

In a pure resistor, the current and voltage are in phase, meaning there is no phase difference between them, which corresponds to an angle of zero degrees.

Question 10

An AC voltage source,with a peak output of 72 V,results in dissipation of energy in a resistor at rate of 140 W.What is the value of the resistance?

Accepted Answer

The answer of An AC voltage source,with a peak output...

Question 11

In the inductor of a 59-Hz AC series circuit,the peak voltage precedes the peak current in each cycle by what time interval?

Accepted Answer

The time interval between the peak voltage and the peak current in an inductor in an AC series circuit is given by:

δt = π/2f

where f is the frequency of the AC circuit. Substituting f = 59 Hz, we get:

δt = π/2(59) ≈ 4.2E-3 s

Therefore, the correct choice is B.

Question 12

In the typical household AC voltage of 311 V,what is the peak voltage?

Accepted Answer

The peak voltage (V_peak) in an AC system is given by V_peak = V_rms * sqrt(2), where V_rms is the root mean square voltage, typically given as the household AC voltage. For 311 V, V_peak = 311V * sqrt(2) ≈ 440 V.

Question 13

The peak voltage of an AC source is 296 V.What is the rms voltage?

Accepted Answer

The relation between peak voltage and rms voltage is given as V_rms = V_peak / √2. Putting in the values we get, V_rms = 296 / √2 = 209 V (approx). Therefore, the correct option is C.

Question 14

The rate of heat dissipation in an AC circuit with resistance,R,and effective current,I_rms,is given by which of the following?

Accepted Answer

The rate of heat dissipation in an AC circuit is given by formula P = V^2/R, where V is the effective voltage across the circuit. We know that V = Ieff * R, where Ieff is the effective current of the AC circuit. So we can substitute V in the formula for P and get: P = (Ieff * R)^2 / R Simplifying this, we get: P = Ieff^2 * R Substituting the given values, we get: P = (I_rms)^2 / R which is equivalent to option B.

Question 15

An AC voltage source,with a peak output of 122 V,is connected to a 54.0-Ω resistor.What is the rate of energy dissipated due to heat in the resistor?

Accepted Answer

The answer of An AC voltage source,with a peak output...

Question 16

In an AC circuit operating at a frequency where the phase angle with respect to the current is 30°,what happens to the phase angle if the capacitance of the circuit is increased?

Accepted Answer

When capacitance is increased in an AC circuit, the reactance of the capacitor decreases. This leads to an increase in the current flowing through the circuit. As a result, the phase angle between the voltage and current increases. Therefore, the answer is A, the phase angle increases.

Question 17

The peak voltage of an AC source is 400 V.What is the rms voltage?

Accepted Answer

The rms voltage is calculated as the peak voltage divided by the square root of 2. Therefore, 400 V / √2 ≈ 283 V.

Question 18

In an AC series circuit the capacitive reactance is 217 Ω and frequency is 56 Hz.What is the capacitance?

Accepted Answer

We know that capacitive reactance (Xc) is given by Xc = 1/(2πfC), where f is the frequency and C is the capacitance.

Substituting the given values, we have:

217 = 1/(2π*56*C)

C = 1/(2π*56*217)

C = 1.31E-5 F

Therefore, the capacitance is 1.31E-5 F, which corresponds to choice C.

Question 19

In an AC series circuit the inductive reactance is 41.0 Ω and the frequency is 137 Hz.What is the inductance in the circuit?

Accepted Answer

The inductive reactance (XL) in an AC circuit is given by the formula XL = 2πfL, where f is the frequency and L is the inductance. Rearranging the formula to solve for L gives L = XL / (2πf). Substituting the given values (XL = 41.0 Ω, f = 137 Hz) into the formula yields L = 41.0 / (2 * π * 137) ≈ 4.8E-2 H.

Question 20

A 13.7-μF capacitor is connected to an AC source with an rms voltage of 148 V and a frequency of 40.0 Hz.What is the rms current in the capacitor?

Accepted Answer

The rms current in a capacitor can be calculated using the formula:

Irms = Vrms / Xc

where Xc is the capacitive reactance given by:

Xc = 1 / (2πfC)

Substituting the given values, we get:

Xc = 1 / (2π(40.0 Hz)(13.7×10^-6 F)) = 292.3 Ω

And:

Irms = Vrms / Xc = (148 V) / (292.3 Ω) = 0.509 A

Therefore, the answer is choice C, 0.509 A.

Quiz 21: Alternating-Current Circuits and Electromagnetic Waves

What is the effective (rms) current value for an AC current with an amplitude of 15.4 A?

When a 47-μF capacitor is attached to an AC source,its capacitive reactance is 42.0 Ω.If instead a 150-μF capacitor is attached to the same source,what will be its capacitive reactance?

An AC voltage source,with a peak output of 114 V,is connected to a 40.0-Ω resistor.What is the effective (or rms) current in the circuit?

In a capacitor in an AC circuit,the voltage:

The frequency in an AC series circuit is quadrupled.By what factor does this change the capacitive reactance?

A 400-Ω resistor and a capacitor are connected in parallel across a 300-Hz source.If the amplitude of the current in the resistor is equal to that in the capacitor,what is the value of the capacitance?

The rms current is equal to the direct current that:

The current in an inductor connected to an AC voltage source lags the voltage.This lag is caused by the:

In an AC series circuit,the current in a pure resistor differs in phase with the applied voltage by what angle?

An AC voltage source,with a peak output of 72 V,results in dissipation of energy in a resistor at rate of 140 W.What is the value of the resistance?

In the inductor of a 59-Hz AC series circuit,the peak voltage precedes the peak current in each cycle by what time interval?

In the typical household AC voltage of 311 V,what is the peak voltage?

The peak voltage of an AC source is 296 V.What is the rms voltage?

The rate of heat dissipation in an AC circuit with resistance,R,and effective current,I_rms,is given by which of the following?

An AC voltage source,with a peak output of 122 V,is connected to a 54.0-Ω resistor.What is the rate of energy dissipated due to heat in the resistor?

In an AC circuit operating at a frequency where the phase angle with respect to the current is 30°,what happens to the phase angle if the capacitance of the circuit is increased?

The peak voltage of an AC source is 400 V.What is the rms voltage?

In an AC series circuit the capacitive reactance is 217 Ω and frequency is 56 Hz.What is the capacitance?

In an AC series circuit the inductive reactance is 41.0 Ω and the frequency is 137 Hz.What is the inductance in the circuit?

A 13.7-μF capacitor is connected to an AC source with an rms voltage of 148 V and a frequency of 40.0 Hz.What is the rms current in the capacitor?

Quiz 21: Alternating-Current Circuits and Electromagnetic Waves

What is the effective (rms) current value for an AC current with an amplitude of 15.4 A?

When a 47-μF capacitor is attached to an AC source,its capacitive reactance is 42.0 Ω.If instead a 150-μF capacitor is attached to the same source,what will be its capacitive reactance?

An AC voltage source,with a peak output of 114 V,is connected to a 40.0-Ω resistor.What is the effective (or rms) current in the circuit?

In a capacitor in an AC circuit,the voltage:

The frequency in an AC series circuit is quadrupled.By what factor does this change the capacitive reactance?

A 400-Ω resistor and a capacitor are connected in parallel across a 300-Hz source.If the amplitude of the current in the resistor is equal to that in the capacitor,what is the value of the capacitance?

The rms current is equal to the direct current that:

The current in an inductor connected to an AC voltage source lags the voltage.This lag is caused by the:

In an AC series circuit,the current in a pure resistor differs in phase with the applied voltage by what angle?

An AC voltage source,with a peak output of 72 V,results in dissipation of energy in a resistor at rate of 140 W.What is the value of the resistance?

In the inductor of a 59-Hz AC series circuit,the peak voltage precedes the peak current in each cycle by what time interval?

In the typical household AC voltage of 311 V,what is the peak voltage?

The peak voltage of an AC source is 296 V.What is the rms voltage?

The rate of heat dissipation in an AC circuit with resistance,R,and effective current,Irms,is given by which of the following?

An AC voltage source,with a peak output of 122 V,is connected to a 54.0-Ω resistor.What is the rate of energy dissipated due to heat in the resistor?

In an AC circuit operating at a frequency where the phase angle with respect to the current is 30°,what happens to the phase angle if the capacitance of the circuit is increased?

The peak voltage of an AC source is 400 V.What is the rms voltage?

In an AC series circuit the capacitive reactance is 217 Ω and frequency is 56 Hz.What is the capacitance?

In an AC series circuit the inductive reactance is 41.0 Ω and the frequency is 137 Hz.What is the inductance in the circuit?

A 13.7-μF capacitor is connected to an AC source with an rms voltage of 148 V and a frequency of 40.0 Hz.What is the rms current in the capacitor?

The rate of heat dissipation in an AC circuit with resistance,R,and effective current,I_rms,is given by which of the following?