Alternating Current

An AC voltage \(V = 200\sin(100\pi t)\ \text{V}\) is applied. The rms value is:

1. a\(100\ \text{V}\)
2. b\(200\ \text{V}\)
3. c\(\dfrac{200}{\sqrt{2}}\ \text{V}\)
4. d\(100\pi\ \text{V}\)

The reactance of an inductor at frequency \(f\) and inductance \(L\) is:

1. a\(\dfrac{1}{\omega L}\)
2. b\(\omega L\)
3. c\(L^{2}\omega\)
4. d\(\omega^{2} L\)

The reactance of a capacitor of \(C\) at frequency \(f\) is:

1. a\(2\pi f C\)
2. b\(\omega C^{2}\)
3. c\(\omega^{2} C\)
4. d\(\dfrac{1}{2\pi f C}\)

In an LCR series circuit at resonance, the impedance equals:

1. a\(\dfrac{1}{\omega C}\)
2. b\(\omega L\)
3. c\(R\)
4. d\(\sqrt{R^{2} + \omega^{2} L^{2}}\)

The resonance frequency of an LC circuit with \(L = 10\ \text{mH}\) and \(C = 10\ \mu\text{F}\) is:

1. a\(\approx 1592\ \text{Hz}\)
2. b\(\approx 503\ \text{Hz}\)
3. c\(\approx 5033\ \text{Hz}\)
4. d\(\approx 16\ \text{Hz}\)

Power dissipated in a pure inductor in AC circuit is:

1. amaximum
2. b\(\dfrac{1}{2} V_{0} I_{0}\)
3. c\(V_{\mathrm{rms}} I_{\mathrm{rms}}\)
4. dzero

An ideal transformer has turns ratio \(N_{p} : N_{s} = 1 : 5\). If the primary has \(220\ \text{V}\), the secondary voltage is:

1. a\(44\ \text{V}\)
2. b\(1100\ \text{V}\)
3. c\(220\ \text{V}\)
4. d\(550\ \text{V}\)

In an AC circuit with \(R\), \(L\), \(C\) in series, the phase angle \(\phi\) by which the applied voltage \(V\) leads the current \(I\) is given by:

1. a\(\sin\phi = \dfrac{R}{Z}\)
2. b\(\tan\phi = \dfrac{R}{X_{L} - X_{C}}\)
3. c\(\tan\phi = \dfrac{X_{L} - X_{C}}{R}\)
4. d\(\cos\phi = \dfrac{Z}{R}\)

Quality factor \(Q\) of a series LCR circuit at resonance is:

1. a\(\dfrac{\omega_{0} C}{R}\)
2. b\(\dfrac{R}{\omega_{0} L}\)
3. c\(\omega_{0} R L\)
4. d\(\dfrac{\omega_{0} L}{R}\)

An AC source \(V = V_{0}\sin\omega t\) is connected to a capacitor \(C\). The current is:

1. a\(V_{0} C\cos\omega t\)
2. b\(\dfrac{V_{0}}{\omega C}\sin(\omega t - \pi/2)\)
3. c\(V_{0}\omega C\sin(\omega t - \pi/2)\)
4. d\(V_{0}\omega C\sin(\omega t + \pi/2)\)

Assertion (A): In a purely resistive AC circuit, the average power dissipated equals \(V_{\mathrm{rms}} I_{\mathrm{rms}}\).

Reason (R): For a purely resistive circuit, the phase angle between voltage and current is zero, so power factor is 1.

1. aBoth A and R are true, and R is the correct explanation for A
2. bBoth A and R are true, but R is NOT the correct explanation for A
3. cA is true, but R is false
4. dA is false, but R is true

Assertion (A): An ideal transformer cannot operate on DC.

Reason (R): A transformer relies on changing magnetic flux through the secondary to induce an emf; a steady DC current produces a constant flux and no induced emf.

1. aBoth A and R are true, and R is the correct explanation for A
2. bBoth A and R are true, but R is NOT the correct explanation for A
3. cA is true, but R is false
4. dA is false, but R is true

Assertion (A): At resonance in a series LCR circuit, the current is maximum.

Reason (R): At resonance, \(X_{L} = X_{C}\), so impedance reduces to \(R\), the smallest possible value.

1. aBoth A and R are true, and R is the correct explanation for A
2. bBoth A and R are true, but R is NOT the correct explanation for A
3. cA is true, but R is false
4. dA is false, but R is true

Assertion (A): Wattless current is the component of current that contributes nothing to power dissipation.

Reason (R): This component is \(90^\circ\) out of phase with the voltage, and \(\cos 90^\circ = 0\) in the power expression.

1. aBoth A and R are true, and R is the correct explanation for A
2. bBoth A and R are true, but R is NOT the correct explanation for A
3. cA is true, but R is false
4. dA is false, but R is true

1. I. The voltage leads the current by \(\pi/2\).
2. II. The reactance is \(X_{L} = \omega L\).
3. III. Average power dissipated is zero.

Which of the above are CORRECT for an inductor in pure-AC circuit?

1. aOnly I
2. bAll three
3. cOnly II and III
4. dOnly I and II

1. I. \(X_{L} = X_{C}\).
2. II. Total impedance equals \(R\).
3. III. Phase angle between \(V\) and \(I\) is zero.

Which of the above are CORRECT at resonance in series LCR?

1. aOnly I
2. bOnly II
3. cAll three
4. dOnly I and II

1. I. Number of turns in secondary \(>\) number in primary.
2. II. Output voltage \(>\) input voltage.
3. III. Output current \(<\) input current.

Which of the above are CORRECT for a step-up transformer?

1. aOnly I
2. bOnly II
3. cOnly I and II
4. dAll three

1. I. For a sinusoidal waveform, \(V_{\mathrm{rms}} = V_{0}/\sqrt{2}\).
2. II. RMS value is the equivalent DC value that would dissipate the same heat in the same resistor.

Which of the above CORRECTLY describe the rms value?

1. aOnly I
2. bBoth I and II
3. cOnly II
4. dNeither

Match each item in List I with its corresponding entry in List II:

1. a(i)-R, (ii)-S, (iii)-P, (iv)-Q
2. b(i)-Q, (ii)-P, (iii)-S, (iv)-R
3. c(i)-P, (ii)-Q, (iii)-R, (iv)-S
4. d(i)-S, (ii)-Q, (iii)-R, (iv)-P

Match List I (the circuit) with List II (the phase of the current \(I\) relative to the applied voltage \(V\)):

1. a(i)-R, (ii)-S, (iii)-P, (iv)-Q
2. b(i)-R, (ii)-P, (iii)-S, (iv)-Q
3. c(i)-Q, (ii)-S, (iii)-P, (iv)-R
4. d(i)-R, (ii)-Q, (iii)-P, (iv)-S

Match each item in List I with its corresponding entry in List II:

1. a(i)-Q, (ii)-P, (iii)-S, (iv)-R
2. b(i)-P, (ii)-Q, (iii)-R, (iv)-S
3. c(i)-S, (ii)-R, (iii)-P, (iv)-Q
4. d(i)-R, (ii)-S, (iii)-P, (iv)-Q

A series LCR circuit has \(R = 10\ \Omega\), \(L = 0.1\ \text{H}\), \(C = 10\ \mu\text{F}\) and is driven at resonance frequency by a \(100\ \text{V}\) (rms) source. The rms current is:

1. a\(100\ \text{A}\)
2. b\(20\ \text{A}\)
3. c\(10\ \text{A}\)
4. d\(1\ \text{A}\)

An AC source \(220\ \text{V}\) (rms), \(50\ \text{Hz}\) drives a \(0.5\ \text{H}\) inductor. The rms current is:

1. a\(220\ \text{A}\)
2. b\(0.7\ \text{A}\)
3. c\(2.8\ \text{A}\)
4. d\(1.4\ \text{A}\)

An ideal step-down transformer has primary input \(2200\ \text{V}\) at \(1\ \text{A}\). Secondary delivers \(220\ \text{V}\). The secondary current is:

1. a\(10\ \text{A}\)
2. b\(0.1\ \text{A}\)
3. c\(1\ \text{A}\)
4. d\(100\ \text{A}\)

For a series RC circuit, the phase angle \(\phi\) between the applied voltage and the current is given by:

1. a\(\tan\phi = \dfrac{X_{C}}{R}\)
2. b\(\tan\phi = \dfrac{R}{X_{C}}\)
3. c\(\tan\phi = X_{C} R\)
4. d\(\sin\phi = R\)

For a series LCR circuit, the current amplitude is plotted against the angular frequency of the source. The peak of this curve corresponds to:

1. a\(\omega_{0} = \dfrac{L}{C}\)
2. b\(\omega_{0} = \dfrac{1}{LC}\)
3. cresonance frequency \(\omega_{0} = \dfrac{1}{\sqrt{LC}}\)
4. d\(\omega_{0} = LC\)

Based on the passage, the impedance of the circuit is:

1. a\(10\ \Omega\)
2. b\(30\ \Omega\)
3. c\(70\ \Omega\)
4. d\(50\ \Omega\)

Based on the passage, the rms current is:

1. a\(2\ \text{A}\)
2. b\(4\ \text{A}\)
3. c\(6\ \text{A}\)
4. d\(8\ \text{A}\)

Based on the passage, the average power dissipated is:

1. a\(160\ \text{W}\)
2. b\(320\ \text{W}\)
3. c\(480\ \text{W}\)
4. d\(800\ \text{W}\)

Based on the passage, the power factor is:

1. a0.8
2. b0.6
3. c0.5
4. d1.0