Class 12 Alternating Current Mock Test (CBSE)

Topics in Alternating Current

• AC voltage applied to a resistor
• Representation of AC current and voltage by phasors
• AC voltage applied to an inductor
• AC voltage applied to a capacitor
• AC voltage applied to a series LCR circuit
• Resonance
• Power in AC circuit and power factor
• Transformers

Alternating Current practice questions with answers

1. Q1Multiple choice·1 mark
   In an alternating current circuit containing only a pure inductor, the current:

   1. (a)leads the voltage by a phase angle of $\pi/2$
   2. (b)lags behind the voltage by a phase angle of $\pi$
   3. (c)lags behind the voltage by a phase angle of $\pi/2$
   4. (d)is in phase with the voltage
   Show answer and step marks

   1. Correct option: (c) lags behind the voltage by a phase angle of $\pi/2$+1

   Answer: (c)
2. Q2Multiple choice·1 mark
   When the frequency of the AC source connected to a pure capacitor is doubled, the capacitive reactance of the circuit:

   1. (a)is halved
   2. (b)is doubled
   3. (c)becomes four times
   4. (d)remains unchanged
   Show answer and step marks

   1. Correct option: (a) is halved+1

   Answer: (a)
3. Q3Short answer·3 marks
   An AC source of voltage $V = 220\sin(100t)\text{ V}$ is connected across a series combination of a resistor $R = 30\ \Omega$ and an inductor of inductive reactance $X_L = 40\ \Omega$. (a) Find the impedance of the circuit and the peak current. (b) Calculate the power factor of the circuit and the average power dissipated per cycle.
   Show answer and step marks

   1. Impedance $Z = \sqrt{R^2 + X_L^2} = \sqrt{30^2 + 40^2} = 50\ \Omega$.+0.5
   2. Peak current $I_0 = \frac{V_0}{Z} = \frac{220}{50} = 4.4\text{ A}$.+0.5
   3. Power factor $\cos\phi = \frac{R}{Z} = \frac{30}{50} = 0.6$.+1
   4. Average power $P_{\text{avg}} = V_{\text{rms}} I_{\text{rms}} \cos\phi = \left(\frac{220}{\sqrt{2}}\right) \left(\frac{4.4}{\sqrt{2}}\right) (0.6) = 290.4\text{ W}$.+1

   Answer: (a) $Z = 50\ \Omega$, $I_0 = 4.4\text{ A}$ (b) $\cos\phi = 0.6$, $P_{\text{avg}} = 290.4\text{ W}$
4. Q4Short answer·3 marks
   A series $LCR$ circuit contains a pure inductor of inductance $L = 5.0\text{ H}$, a capacitor of capacitance $C = 80\ \mu\text{F}$, and a resistor of resistance $R = 40\ \Omega$, connected to a variable frequency AC source of peak voltage $V_0 = 220\text{ V}$. (a) Find the angular frequency and the frequency of the AC source at which resonance occurs. (b) Calculate the impedance of the circuit and the maximum current amplitude at resonance.
   Show answer and step marks

   1. Resonant angular frequency $\omega_r = \frac{1}{\sqrt{LC}} = \frac{1}{\sqrt{5.0 \times 80 \times 10^{-6}}} = 50\text{ rad/s}$.+0.5
   2. Resonant frequency $f_r = \frac{\omega_r}{2\pi} = \frac{25}{\pi}\text{ Hz} \approx 7.96\text{ Hz}$.+0.5
   3. At resonance, the impedance of the circuit equals its resistance: $Z = R = 40\ \Omega$.+1
   4. Maximum current amplitude $I_0 = \frac{V_0}{Z} = \frac{220}{40} = 5.5\text{ A}$.+1

   Answer: (a) $\omega_r = 50\text{ rad/s}$, $f_r = \frac{25}{\pi}\text{ Hz}$ (b) $Z = 40\ \Omega$, $I_0 = 5.5\text{ A}$

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