Alternating Current PYQs Set 10 (PDF)

Set 10 of 10 · Questions 271-290 of 290

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Mere Teacher · Previous Year Questions JEE Main Physics · Alternating Current · Set 10 (Q271-290)
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271. $The electric current in the circuit is given as i = i_{0} (t / T) . The r.m.s current for the period t = 0 to t = T is ____ .$ (1) $i_{o}$ (2) $\frac{i _{0}}{6}$ (3) $\frac{i _{0}}{3}$ (4) $\frac{i _{0}}{2}$ 272. $A transformer works on the principle of$ (1) $self-induction$ (2) $electrical inertia$ (3) $magnetic effect of electric current$ (4) $mutual induction$ 273. $When an inductor of inductance \frac{6}{π} H, a capacitor of capacitance \frac{50}{π} μF and resistor of resistance R are connected in series with an AC supply of rms voltage 220 V and frequency 50 Hz, the rms current through the circuit is 440 mA . Match the inductive reactance, XL the capacitive reactance, XC the resistance R and the impedance Z of the circuit given in List-I with the corresponding values given in List-II. LIST-I (A) XL (B) XC (C) R (D) Z LIST-II (I) 200 Ω (II) 300 Ω (III) 500 Ω (IV) 600 Ω$ (1) $(A) - (IV), (B) - (II), (C) - (I), (D) - (III)$ (2) $(A) - (IV), (B) - (III), (C) - (I), (D) - (II)$ (3) $(A) - (IV), (B) - (I), (C) - (II), (D) - (III)$ (4) $(A) - (I), (B) - (IV), (C) - (III), (D) - (II)$ 274. $AC voltage V (t) = 20 sin Ω t of frequency 50Hz is applied to a parallel plate capacitor. The separation between the plates is 2mm and the area is 1 m^{2} . The amplitude of the oscillating displacement current for the applied AC voltage is ___ [Take ϵ_{0} = 8.85 \times 1 0^{- 12} F / m]$ (1) $21.14 μA$ (2) $83.37 μA$ (3) $27.79 μA$ (4) $55.58 μA$ 275. $What happens to the inductive reactance and the current in a purely inductive circuit if the frequency is halved?$ (1) $Both, inductive reactance and current will be halved.$ (2) $Inductive reactance will be halved and current will be doubled.$ (3) $Inductive reactance will be doubled and current will be halved.$ (4) $Both, inducting reactance and current will be doubled.$ 276. $In series LCR circuit at resonance, the phase difference between voltage and current is$ (1) $zero$ (2) $π$ (3) $π /4$ (4) $π /2$ 277. $Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury tube, the tube will be damaged. Reason (R): By using the choke coil, the voltage across the tube is reduced by a factor \frac{R}{R ^{2} + ω ^{2} L ^{2}}, where ω is frequency of the supply across resistor R and inductor L. If the choke coil were not used, the voltage across the resistor would be the same as the applied voltage. choose the most appropriate answer from the options given below:$ (1) $(A) is true but (R) is false$ (2) $Both (A) and (R) are true and (R) is the correct explanation of (A)$ (3) $(A) is false but (R) is true$ (4) $Both (A) and (R) are true but (R) is not the correct explanation of (A)$ 278. $The rms value of current in a 50 Hz AC circuit is 6 A . The average value of AC current over a cycle is$ (1) $62$ (2) $\frac{3}{π 2}$ (3) $Zero$ (4) $\frac{6}{π 2}$ 279. $In a series LCR resonance circuit, if we change the resistance only, from a lower to higher value:$ (1) $The bandwidth of resonance circuit will increase.$ (2) $The resonance frequency will increase.$ (3) $The quality factor will increase.$ (4) $The quality factor and the resonance frequency will remain constant.$ 280. $An alternating voltage source V = 260 sin (628t) is connected across a pure inductor of 5 mH. Inductive reactance in the circuit is:$ (1) $3.14 Ω$ (2) $6 28 Ω$ (3) $0.5 Ω$ (4) $0.318 Ω$ 281. $An electric heater rated 220 V and 550 W is connected to A.C. mains. The current drawn by it is$ (1) $0.8 A$ (2) $2.5 A$ (3) $0.4 A$ (4) $1.25 A$ 282. $In an ac circuit, an inductor, a capacitor and a resistor are connected in series with X_{L} = R = X_{C} Impedance of this circuit is:$ (1) $2 R^{2}$ (2) $Zero$ (3) $R$ (4) $R 2$ 283. $Match List-I with List II List I (A) Phase difference between current and voltage in a purely resistive AC circuit (B) Phase difference between current and voltage in a pure inductive AC circuit (C) Phase difference between current and voltage in a pure capacitive AC circuit (D) Phase difference between current and voltage in an LCR series circuit List II (I) π 2; current leads voltage (II) Zero (III) π 2; current lags voltage (IV) tan^{- 1} (\frac{X _{C} - X _{L}}{R})$ (1) $(A) - (I), (B) - (III), (C) - (IV), (D) - (II)$ (2) $(A) - (II), (B) - (IV), (C) - (III), (D) - (I)$ (3) $(A) - (II), (B) - (III), (C) - (IV), (D) - (I)$ (4) $(A) - (II), (B) - (III), (C) - (I), (D) - (IV)$ 284. $In a circuit consisting of a capacitance and a generator with alternating emf E_{g} = E_{g_{0}} sin ω t, V_{C} and I_{C} are the voltage and current. Correct phasor diagram for such circuit is:$ (1) (2) (3) (4) 285. $In the circuit shown, the voltage V_{1}, across capacitor C$ (1) $is in phase with the source voltage V$ (2) $leads the source voltage V by 90^{\circ}$ (3) $leads the source voltage V by an angle between 0^{\circ} and 90^{\circ}$ (4) $lags behind the source voltage V by an angle between 0^{\circ} and 90^{\circ} .$ 286. $The reciprocal of the total effective resistance of LCR a.c. circuit is called$ (1) $impedance$ (2) $admittance$ (3) $resistance$ (4) $inductive and capacitive reactance$ 287. $Match the List-I with List-II. List I (A) AC generator (B) Transformer (C) Resonance phenomenon to occur (D) Sharpness of resonance List II (I) Presence of both L and C (II) Electromagnetic Induction (III) Quality factor (IV) Mutual Inductance Choose the correct answer from the options given below:$ (1) $A-IV, B-II, C-I, D-III$ (2) $A-II, B-I, C-III, D-IV$ (3) $A-II, B-IV, C-I, D-III$ (4) $A-IV, B-III, C-I, D-II$ 288. $Given below are two statements: Statement-I: The reactance of an ac circuit is zero. It is possible that the circuit contains a capacitor and an inductor. Statement-II: In ac circuit, the average poser delivered by the source never becomes zero. In the light of the above statements, choose the correct answer from the options given below:$ (1) $Both Statement I and Statement II are true.$ (2) $Both Statement I and Statement II are false.$ (3) $Statement I is true but Statement II in false.$ (4) $Statement I is false but Statement II is true.$ 289. $In the given circuit, the magnitude of V_{L} and Vc are twice that of vr. Given that f = 50Hz, the inductance of the coil is \frac{1}{Kπ} mH . The value of K is ________ .$ 290. $The frequencies at which the current amplitude in an LCR series circuit becomes \frac{1}{2} times its maximum value, are 212 rad s-1 and 232 rad s-1. The value of resistance in the circuit is R = 5 Ω . The self inductance in the circuit is________mH.$