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Physics XII: Alternating Current
Exercise Solutions & Explanations
Exercise Questions (1 - 8)
1. The r.m.s. value of a sine wave is 100 A. Its peak value is:
Answer: (B) 141.4 A
The relationship between Root Mean Square (Irms) and Peak current (I 0 ) is given by Irms = I 0 / √2. To find the peak value: I 0 = Irms × √2 = 100 × 1.414 = 141.4 A.
2. A sine wave has a frequency of 50 Hz. Its angular frequency is:
Answer: (A) 100 π
Angular frequency (ω) is calculated using the formula ω = 2πf. Given f = 50 Hz, then ω = 2π(50) = 100π rad/s.
3. The power factor of a purely resistive circuit is:
Answer: (B) unity
In a purely resistive circuit, voltage and current are in phase (phase angle φ = 0°). The power factor is cos(φ). Since cos(0°) = 1, the power factor is unity.
4. A capacitor is a perfect insulator for:
Answer: (A) Direct current
The capacitive reactance is XC = 1 / (2πfC). For DC, the frequency (f) is zero, making XC infinite. Therefore, a capacitor blocks DC once fully charged.
5. The peak value of alternating current is 5√2 A. The mean square value of current will be:
Answer: (A) 5 A
The RMS (Root Mean Square) value is calculated as Irms = I 0 / √2. Substituting the given value: Irms = (5√2) / √2 = 5 A.
6. In a choke coil, the reactance XL and resistance R are related as:
Answer: (C) XL » R
A choke coil is designed to limit AC current with minimum power loss. This is achieved by having high inductance (high XL) and very low ohmic resistance (R).
7. The phase difference between the current and voltage at resonance is:
Answer: (A) 0
At resonance, inductive reactance equals capacitive reactance (XL = XC). The circuit becomes purely resistive, so the phase difference between voltage and current is zero.
8. In an AC system we generate sine wave form because:
Answer: (B) It produces least disturbance in electrical circuits
Sine waves are "pure" frequencies. Other waveforms (square, triangular) contain harmonics that cause interference, power loss, and mechanical vibration in electrical machinery.
Exercise Questions (9 - 15)
9. An alternating voltage is given by 20sin(157t). The frequency of alternating voltage is:
Answer: (B) 25 Hz
When voltage and current are in phase, the phase angle φ is 0. The power factor is cos(0), which equals 1.
15. With increase in frequency of an AC supply, the impedance of an RLC series circuit:
Answer: (D) capacitive reactance XC decreases only
As frequency increases, XL increases and XC decreases. While total impedance Z follows a U-shaped curve (decreasing then increasing), choice (D) is the most specific correct description of an individual component's behavior.
Physics Grade XII - Unit 15: Alternating Current
