Alternating current 1

All of the following have the same units except:

• inductance.

• capacitive reactance.

• impedance.

• resistance.

Answer explanation

Inductance is measured in henries (H), while capacitive reactance, impedance, and resistance are measured in ohms (Ω). Therefore, inductance is the only option that does not share the same units as the others.

A resistor is connected to an AC power supply. On this circuit, the current

• leads the voltage by 90°.

• lags the voltage by 90°.

• is in phase with the voltage.

• none of the given answers

Answer explanation

In a resistor connected to an AC power supply, the current is in phase with the voltage. This means that the peaks and zero crossings of both the current and voltage occur at the same time.

A pure inductor is connected to an AC power supply. In this circuit, the current

• leads the voltage by 90°.

• lags the voltage by 90°.

• is in phase with the voltage.

• none of the given answers.

Answer explanation

In a pure inductor, the current lags the voltage by 90° due to the nature of inductance, where the voltage reaches its peak before the current does. Therefore, the correct answer is that the current lags the voltage by 90°.

If the frequency of the AC voltage across an inductor is doubled, the inductive reactance of that inductor

• increases to 4 times its original value.

• increases to twice its original value.

• decreases to one-half its original value.

• decreases to one-fourth its original value.

Answer explanation

Inductive reactance (X_L) is given by the formula X_L = 2πfL. If the frequency (f) is doubled, X_L becomes 2π(2f)L = 2(2πfL), which means it increases to twice its original value.

The formula for inductive reactance is

Answer explanation

The formula for inductive reactance is given by \(X_L = \omega L\), where \(\omega\) is the angular frequency and \(L\) is the inductance. Thus, the correct answer is \(\omega L\).

The instantaneous current in an ac circuit is i=2.0 sin314t, what is its frequency?

• 100 Hz

• 60 Hz

• 50 Hz

• 2π

Answer explanation

The given current equation is i=2.0 sin(314t). The angular frequency \( \omega \) is 314 rad/s. The frequency \( f \) is given by \( f = \frac{\omega}{2\pi} = \frac{314}{2\pi} \approx 50 \) Hz.

The instantaneous current in an ac circuit is i=2.0 sin314t, what is rms value of the current.

• 1.414 A

• 2.828A

• 1 A

• 2 A

Answer explanation

The rms value of an ac current is given by I_rms = I_0 / √2. Here, I_0 = 2.0 A, so I_rms = 2.0 / √2 = 1.414 A. Thus, the correct answer is 1.414 A.

An inductor of inductance 22.0 mH is connected to an a.c. supply with frequency f. If the reactance of the inductor is 660 Ω, what is the value of f?

• 3.00undefined Hz

• 4.77undefined Hz

• 7.16undefined Hz

Answer explanation

The reactance of an inductor is given by X_L = 2πfL. Rearranging gives f = X_L / (2πL). Substituting L = 22.0 mH and X_L = 660 Ω, we find f ≈ 4.77 Hz, which matches the correct answer.

In an AC circuit, if the voltage is given by v=5.0 sin(628t), what is the peak voltage?

• 5.0 V

• 2.5 V

• 0 V

• 10 V

Answer explanation

The voltage function v=5.0 sin(628t) indicates that the peak voltage is the coefficient of the sine function, which is 5.0 V. Therefore, the correct answer is 5.0 V.

What is the phase difference between the current and voltage in a purely resistive AC circuit?

• 0°

• 45°

• 90°

• 180°

Answer explanation

In a purely resistive AC circuit, the current and voltage are in phase, meaning they reach their maximum and minimum values simultaneously. Therefore, the phase difference is 0°, making the correct answer 0°.