physics : class12 Inductive Current Lag : Wattless Current : Electromagnetic Induction and Alternating Currents MCQ Questions and Answers
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Inductive Current Lag
MCQ questions and answers.
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MCQ Questions
1. An ideal inductor is connected to a sinusoidal source whose voltage is v(t) = V₀ sin(ωt). In the steady state, which expression correctly represents the current through the inductor?
A.
i(t) = (V₀/ωL) sin(ωt)
B.
i(t) = (V₀/ωL) sin(ωt + π/2)
C.
i(t) = (V₀/ωL) sin(ωt - π/2)
D.
i(t) = (V₀/L) sin(ωt - π/2)
Correct Answer:
i(t) = (V₀/ωL) sin(ωt - π/2)
Explanation:
For an ideal inductor, v = L(di/dt). Integrating v(t) = V₀ sin(ωt) gives i(t) = -(V₀/ωL) cos(ωt), which is equivalent to (V₀/ωL) sin(ωt - π/2). Thus, current lags voltage by 90°.
2. A pure inductor is connected to an AC source of frequency f. If the frequency is increased to 3f while the voltage amplitude remains unchanged, what happens to the current amplitude and the phase lag?
A.
Current amplitude becomes three times larger and the lag becomes 30°
B.
Current amplitude becomes one-third and the lag remains 90°
C.
Current amplitude remains unchanged and the lag becomes 270°
D.
Current amplitude becomes one-third and the lag becomes 45°
Correct Answer:
Current amplitude becomes one-third and the lag remains 90°
Explanation:
For a pure inductor, inductive reactance is X_L = ωL, so current amplitude I₀ = V₀/(ωL). Tripling frequency reduces current amplitude to one-third. The phase relation remains a 90° lag because an ideal inductor always produces a current lag of π/2.
3. In a series RL circuit, the current lags the applied voltage by 60°. If the resistance is 20 Ω, what is the inductive reactance?
A.
11.55 Ω
B.
20.00 Ω
C.
34.64 Ω
D.
40.00 Ω
Correct Answer:
34.64 Ω
Explanation:
For a series RL circuit, tan φ = X_L/R. With φ = 60° and R = 20 Ω, X_L = R tan 60° = 20√3 ≈ 34.64 Ω. This reactance causes the current to lag the voltage by 60°.
4. The voltage across a pure inductor is v(t) = 100 sin(200t) V, and its inductance is 0.50 H. What is the amplitude of the current and its phase relative to the voltage?
A.
1.0 A, current leads voltage by 90°
B.
1.0 A, current lags voltage by 90°
C.
0.5 A, current lags voltage by 45°
D.
2.0 A, current lags voltage by 90°
Correct Answer:
1.0 A, current lags voltage by 90°
Explanation:
The inductive reactance is X_L = ωL = 200 × 0.50 = 100 Ω. Therefore, current amplitude is I₀ = V₀/X_L = 100/100 = 1.0 A. In a pure inductor, current lags voltage by 90°.
5. In a series RL circuit, the applied voltage and current are represented by V = 100∠0° V and I = 5∠−37° A, respectively. What are the resistance and inductive reactance of the circuit?
A.
R = 16 Ω and X_L = 12 Ω
B.
R = 12 Ω and X_L = 16 Ω
C.
R = 20 Ω and X_L = 15 Ω
D.
R = 15 Ω and X_L = 20 Ω
Correct Answer:
R = 16 Ω and X_L = 12 Ω
Explanation:
The impedance is Z = V/I = 100/5 = 20 Ω with phase angle +37° because voltage leads current. Thus, R = Z cos 37° ≈ 20 × 0.8 = 16 Ω and X_L = Z sin 37° ≈ 20 × 0.6 = 12 Ω. The positive impedance angle indicates inductive current lag.
6. A sinusoidal current in a pure inductor is i(t) = I₀ cos(ωt). Which voltage expression is consistent with this current?
A.
v(t) = −ωLI₀ sin(ωt)
B.
v(t) = ωLI₀ sin(ωt)
C.
v(t) = ωLI₀ cos(ωt)
D.
v(t) = −(I₀/ωL) sin(ωt)
Correct Answer:
v(t) = −ωLI₀ sin(ωt)
Explanation:
For an inductor, v = L(di/dt). Differentiating i(t) = I₀ cos(ωt) gives di/dt = −ωI₀ sin(ωt), so v(t) = −ωLI₀ sin(ωt). This voltage leads the current by 90°, equivalently the current lags the voltage by 90°.
7. A series RL circuit has a phase angle of 53° between its voltage and current. If the current is 4 A and the resistance is 15 Ω, what is the applied voltage approximately?
A.
60 V
B.
75 V
C.
100 V
D.
125 V
Correct Answer:
100 V
Explanation:
For an RL circuit, cos φ = R/Z. Hence Z = R/cos 53° ≈ 15/0.6 = 25 Ω. The applied voltage is V = IZ = 4 × 25 = 100 V. The positive phase angle corresponds to the current lagging the voltage.
8. An ideal inductor is initially carrying no current and is suddenly connected to a sinusoidal voltage source v(t) = V₀ sin(ωt). Which statement correctly describes the steady-state current after transients are excluded?
A.
It is in phase with the voltage and has amplitude V₀/(ωL)
B.
It leads the voltage by 90° and has amplitude V₀/(ωL)
C.
It lags the voltage by 90° and has amplitude V₀/(ωL)
D.
It lags the voltage by 45° and has amplitude V₀/L
Correct Answer:
It lags the voltage by 90° and has amplitude V₀/(ωL)
Explanation:
The steady-state solution of v = L(di/dt) for a sinusoidal voltage has current amplitude V₀/(ωL) and phase −90° relative to voltage. The initial switching condition can introduce a transient or constant component, but it does not alter the steady-state inductive lag.
9. In a series RL circuit, the current lags the applied voltage by 30°. If the frequency is doubled while R and L remain unchanged, which statement is correct?
A.
The lag becomes 15° because the current amplitude decreases
B.
The lag becomes greater than 30° because X_L increases
C.
The lag remains 30° because phase angle is independent of frequency
D.
The lag becomes less than 30° because the resistance becomes dominant
Correct Answer:
The lag becomes greater than 30° because X_L increases
Explanation:
For a series RL circuit, tan φ = ωL/R. Doubling frequency doubles X_L = ωL, so tan φ increases and therefore the phase angle φ increases. The current consequently lags the applied voltage by an angle greater than 30°.
10. Two series RL circuits are connected to the same sinusoidal voltage source. Circuit P has R = 12 Ω and X_L = 5 Ω, while circuit Q has R = 5 Ω and X_L = 12 Ω. Which circuit has the larger current lag, and what are the approximate lag angles?
A.
Circuit P; 22.6° for P and 67.4° for Q
B.
Circuit Q; 22.6° for P and 67.4° for Q
C.
Circuit P; 67.4° for P and 22.6° for Q
D.
Both have equal lag because their impedances are equal
Correct Answer:
Circuit Q; 22.6° for P and 67.4° for Q
Explanation:
For a series RL circuit, tan φ = X_L/R. For P, tan φ = 5/12, giving φ ≈ 22.6°. For Q, tan φ = 12/5, giving φ ≈ 67.4°. Therefore, circuit Q has the larger inductive current lag.
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