Free Circuit Analysis MCQs with Answers

• A. the more heat than produced by A.C. when flowing through the same circuit
• B. the same heat as produced by A.C. when flowing through the same circuit
• C. the less heat than produced by A.C. flowing through the same circuit
• D. none of the above

Explanation: RMS current is the equivalent DC current that produces the same heating effect in the same resistance over the same time.

• A. falls to 36.8% of its final steady value
• B. rises to 38.6% of its final steady value
• C. rises to 63.2% of its final steady value
• D. none of the above

Explanation: For capacitor charging, one time constant changes the voltage to 1 - e^-1, or about 63.2%, of its final value.

• A. r.m.s. value is equal to average value
• B. r.m.s. value of current is greater than average value
• C. r.m.s. value of current is less than average value
• D. none of the above

Explanation: A square wave has constant magnitude during each interval, so its RMS magnitude and average rectified magnitude are equal.

• A. oscillating
• B. square wave
• C. sinusoidal
• D. non-oscillating

Explanation: With no resistance, an RLC circuit has no damping, so energy transfers repeatedly between the inductor and capacitor.

• A. resistance
• B. inductance
• C. capacitance
• D. both B. and C.

Explanation: For a pure inductor or pure capacitor, the phase angle is 90°, so power factor cos 90° equals zero.

• A. consumes some power on average
• B. does not take power at all from a line
• C. takes power from the line during some part of the cycle and then returns back to it during other part of the cycle
• D. none of the above

Explanation: A pure inductor absorbs energy while the current is increasing and returns it to the source while the current is decreasing.

• A. directly as the cross-sectional area of magnetic core
• B. directly as square of number of turns
• C. directly as the permeability of the core
• D. inversely as the length of the iron path
• E. as A. to (d)

Explanation: For a coil, L = μN²A/l, so inductance increases with core area, permeability, and the square of turns, while decreasing with magnetic-path…

• A. apparent power is equal to the actual power
• B. reactive power is more than the apparent power
• C. reactive power is more than the actual power
• D. actual power is more than its reactive power

Explanation: In a highly capacitive circuit, the phase angle is close to 90°, so reactive power is much larger than active or actual power.

• A. will change the maximum value of current at resonance
• B. will change the resonance frequency
• C. will change the impedance at resonance frequency
• D. will increase the selectivity of the circuit

Explanation: The resonance frequency is unchanged because LC remains constant when L is doubled and C is halved.

• A. capacitance is less and frequency of supply is less
• B. capacitance is less and frequency of supply is more
• C. capacitance is more and frequency of supply is less
• D. capacitance is more and frequency of supply is more

Explanation: Capacitive reactance is Xc = 1/(2πfC), so it becomes larger when both capacitance and supply frequency are smaller.

• A. 0.05 s
• B. 0.005 s
• C. 0.0005 s
• D. 0.5 s

Explanation: Time period is the reciprocal of frequency: T = 1/f = 1/200 = 0.005 s. The other values correspond to different frequencies.

• A. 90
• B. 60
• C. 45
• D. 30

Explanation: For a sine wave, the instantaneous value equals the RMS value when sin θ = 1/√2.

• A. average value/r.m.s. value
• B. average value/peak value
• C. r.m.s. value/average value
• D. r.m.s. value/peak value

Explanation: Form factor compares the heating-equivalent value with the average value, so it is defined as RMS value divided by average value.

• A. 0.636 Emax
• B. 0.707 Emax
• C. 0.434 EWc
• D. lAUEmax

Explanation: The average value of a sine wave over one half-cycle is \(2E_{max}/\pi\), which equals approximately \(0.636E_{max}\).

• A. 0.5 Imax
• B. 0.707
• C. 0.9
• D. 1.414 Lmax

Explanation: For a sinusoidal current, the RMS value is its peak value divided by \(\sqrt{2}\), giving \(I_{rms}=0.707I_{max}\).

• A. 1.414
• B. 0.707
• C. 1.11
• D. 0.637

Explanation: A sine wave has average value \(0.637\) times its peak value and RMS value \(0.707\) times its peak value; their ratio is…

• A. half wave rectified sine wave
• B. triangular wave
• C. sine wave
• D. square wave

Explanation: For equal peak values, the half-wave rectified sine has average value \(E_{max}/\pi\approx0.318E_{max}\), lower than the corresponding…

• A. 180″
• B. 90°
• C. 60°
• D. 0°

Explanation: Average AC power is \(P=VI\cos\phi\); for a passive circuit it becomes zero at a 90° phase difference, so no power is consumed.

• A. 360°
• B. 180°
• C. 90°
• D. 0°

Explanation: Opposite phase means one wave is at its positive peak when the other is at its negative peak, corresponding to a phase separation of 180°.

• A. both will reach their minimum values at the same instant
• B. both will reach their maximum values at the same instant
• C. when one wave reaches its maxi¬mum value, the other will reach its minimum value
• D. none of the above

Explanation: A phase difference of \(\pi\) radians equals 180°, so the waves are oppositely phased.