Physics Objective Questions and Answers: Alternating Current
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Multiple Choice Questions
(a) \( 100\sqrt{10}\ \Omega \)
(b) \( 10\sqrt{10}\ \Omega \)
(c) \( 100\ \Omega \)
(d) \( \sqrt{10}\ \Omega \)
Show Answer & Explanation
Answer: (b) \( 10\sqrt{10}\ \Omega \)
Explanation:
1. X_L = 2π × 50 × 0.1 = 31.4 ohm.
2. Z = √(1 + 31.4²) = 31.4 ohm, nearly 10√10 = 31.6 ohm.
Teacher's Note:
1. Recall the basic relation.
(a) \( \frac{VI}2 \)
(b) \( \frac{VI}{\sqrt2} \)
(c) V I
(d) V I cos θ
Show Answer & Explanation
Answer: (d) V I cos θ
Explanation:
1. P = V_rms I_rms cos θ.
Teacher's Note:
1. Recall the basic relation.
(a) 100 V
(b) \( 50\sqrt2\ \text{V} \)
(c) 50 V
(d) 0 V
Show Answer & Explanation
Answer: (d) 0 V
Explanation:
1. V_L and V_C are exactly opposite in phase and equal, so they cancel and the LC combination has zero voltage.
Teacher's Note:
1. Recall the basic relation.
(a) V0
(b) \( V_0/\sqrt2 \)
(c) V0/2
(d) \( V_0/\sqrt3 \)
Show Answer & Explanation
Answer: (b) \( V_0/\sqrt2 \)
Explanation:
1. V_rms² = (1/T)∫V² dt = (V0² × T/2)/T = V0²/2.
2. So V_rms = V0/√2.
Teacher's Note:
1. Recall the basic relation.
(a) remains constant
(b) increases
(c) decreases
(d) decreases at first, becomes minimum and then increases
Show Answer & Explanation
Answer: (d) decreases at first, becomes minimum and then increases
Explanation:
1. Z is minimum (= R) at resonance.
2. It is larger both below and above the resonance frequency.
Teacher's Note:
1. Recall the basic relation.
(a) The reactance of the capacitor is directly proportional to its ability to store charge
(b) Capacitive reactance is inversely proportional to the frequency of the current
(c) Capacitive reactance is measured in farad
(d) The reactance of a capacitor in an a.c. circuit is similar to the resistance of a capacitor in a d.c. circuit
Show Answer & Explanation
Answer: (b) Capacitive reactance is inversely proportional to the frequency of the current
Explanation:
1. X_C = 1/(2πfC) decreases as the frequency increases.
2. It is measured in ohm and varies inversely with C.
Teacher's Note:
1. Recall the basic relation.
(a) \( \frac{i^2R}{(\omega L-1/\omega C)} \)
(b) zero
(c) \( i^2\omega L \)
(d) \( i^2R \)
Show Answer & Explanation
Answer: (d) \( i^2R \)
Explanation:
1. At resonance the whole circuit behaves as a resistance R, so P = i²R.
Teacher's Note:
1. Recall the basic relation.
(a) 150 V and 2.2 A
(b) 220 V and 2.0 A
(c) 220 V and 2.2 A
(d) 100 V and 2.0 A
Show Answer & Explanation
Answer: (c) 220 V and 2.2 A
Explanation:
1. V_L = V_C means X_L = X_C, so the circuit is at resonance.
2. Then Z = R, I = 220/100 = 2.2 A and V_R = 220 V.
Teacher's Note:
1. Recall the basic relation.
(a) the maximum voltage between the plates is 220 V
(b) the current is in phase with the applied voltage
(c) the charge on the plate is not in phase with the applied voltage
(d) the power delivered to the capacitor per cycle is zero
Show Answer & Explanation
Answer: (d) the power delivered to the capacitor per cycle is zero
Explanation:
1. The peak voltage is 220√2 V and the current leads the voltage by 90°.
2. The charge is in phase with the voltage.
3. The average power over a cycle is zero.
Teacher's Note:
1. Recall the basic relation.
(a) 2 : π
(b) \( 2\sqrt2:\pi \)
(c) \( \sqrt2:\pi \)
(d) \( \sqrt2:1 \)
Show Answer & Explanation
Answer: (b) \( 2\sqrt2:\pi \)
Explanation:
1. Mean over half cycle = 2I0/π and rms = I0/√2.
2. The ratio is 2√2 : π.
Teacher's Note:
1. Recall the basic relation.
(a) 4X
(b) X/2
(c) X/4
(d) 2X
Show Answer & Explanation
Answer: (c) X/4
Explanation:
1. X = 1/(2πfC).
2. Doubling both f and C makes X one fourth.
Teacher's Note:
1. Recall the basic relation.
Assertion (A): In a purely inductive or capacitive circuit, the current is referred to as wattless current.
Reason (R): No power is dissipated in a purely inductive or capacitive circuit even though a current is flowing in the circuit.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation
Answer: (a) Both A and R are true, and R is the correct explanation of A.
Explanation:
1. The average power is V I cos 90° = 0, so the current is called wattless.
2. The reason states exactly why.
Teacher's Note:
1. Average power is zero.
(a) π
(b) π/2
(c) 0
(d) π/3
Show Answer & Explanation
Answer: (b) π/2
Explanation:
1. The current leads the voltage by π/2 in a capacitor.
Teacher's Note:
1. Recall the basic relation.
(a) the circuit contains an ideal inductance only
(b) the circuit contains an ideal resistance only
(c) the circuit contains an ideal inductance and an ideal capacitance only
(d) the circuit contains an ideal capacitance only
Show Answer & Explanation
Answer: (b) the circuit contains an ideal resistance only
Explanation:
1. cos φ = 1 only when there is no net reactance, as in a pure resistance.
Teacher's Note:
1. Recall the basic relation.
(a) increases finitely
(b) decreases finitely
(c) remains constant
(d) none of these
Show Answer & Explanation
Answer: (b) decreases finitely
Explanation:
1. Q = (1/R)√(L/C), which decreases as R increases.
Teacher's Note:
1. Recall the basic relation.
(a) \( 2.5\times10^{-2}\ \text{V} \)
(b) 40 V
(c) 250 V
(d) \( 4\times10^{-3}\ \text{V} \)
Show Answer & Explanation
Answer: (c) 250 V
Explanation:
1. I = 100/1000 = 0.1 A.
2. X_L = X_C = 1/(ωC) = 1/(200 × 2 × 10⁻⁶) = 2500 ohm.
3. V_L = I X_L = 250 V.
Teacher's Note:
1. Recall the basic relation.
(a) V_R + V_L + V_C
(b) \( \sqrt{V_R^2+(V_L-V_C)^2} \)
(c) V_R + V_C - V_L
(d) \( [(V_R+V_L)^2+V_C^2]^{1/2} \)
Show Answer & Explanation
Answer: (b) \( \sqrt{V_R^2+(V_L-V_C)^2} \)
Explanation:
1. V_L and V_C are in opposite phase and V_R is 90° from both.
2. V = √[V_R² + (V_L - V_C)²].
Teacher's Note:
1. Recall the basic relation.
(a) 6.7 mA
(b) 0.67 mA
(c) 100 mA
(d) 67 mA
Show Answer & Explanation
Answer: (b) 0.67 mA
Explanation:
1. The initial current is 15/150 = 0.1 A and τ = L/R = 0.03/150 = 0.2 ms.
2. I = 0.1 e⁻¹/0.2) = 0.1 e⁻⁵ = 0.1/150 = 0.67 mA.
Teacher's Note:
1. Recall the basic relation.
(a) I0 = e0/R
(b) I = e/R
(c) I0 = e0
(d) I0 = R/e0
Show Answer & Explanation
Answer: (a) I0 = e0/R
Explanation:
1. For a resistor I0 = e0/R.
Teacher's Note:
1. Recall the basic relation.
(a) \( \tfrac12LI^2 \)
(b) \( LI^2 \)
(c) \( LI^2/4 \)
(d) zero
Show Answer & Explanation
Answer: (d) zero
Explanation:
1. The current lags the voltage by π/2, so the average power is V I cos(π/2) = 0.
Teacher's Note:
1. Recall the basic relation.
(a) maximum
(b) minimum
(c) zero
(d) infinite
Show Answer & Explanation
Answer: (a) maximum
Explanation:
1. I0 = V0/Z is maximum when Z = R.
Teacher's Note:
1. Recall the basic relation.
(a) iron loss
(b) copper loss
(c) mechanical loss
(d) none of these
Show Answer & Explanation
Answer: (a) iron loss
Explanation:
1. Eddy-current and hysteresis loss in the core is called iron loss.
Teacher's Note:
1. Recall the basic relation.
(a) voltage
(b) current
(c) frequency
(d) none of these
Show Answer & Explanation
Answer: (c) frequency
Explanation:
1. The frequency of the output equals that of the input.
Teacher's Note:
1. Recall the basic relation.
(a) 0 to 0.5
(b) 0.5 to 1
(c) 0 to 1
(d) 1 to 2
Show Answer & Explanation
Answer: (c) 0 to 1
Explanation:
1. cos φ lies between 0 (pure reactance) and 1 (pure resistance).
Teacher's Note:
1. Recall the basic relation.
(a) \( P=\sqrt2E_0I_0 \)
(b) \( P=\frac{E_0I_0}{\sqrt2} \)
(c) P = 0
(d) \( P=\frac{E_0I_0}2 \)
Show Answer & Explanation
Answer: (c) P = 0
Explanation:
1. The phase difference is 90°, so cos φ = 0 and the average power is zero.
Teacher's Note:
1. Recall the basic relation.
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Multiple Choice Questions (MCQs) for JEE Physics Alternating Current
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