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Alternating Current · Question 3

JEE Main 2026 (Online) 5th April Evening ShiftNumericalEasy📈 Topic in 6% papers+4
1

A series LCR circuit with R=20 , L=1.6 H and C=40 F is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is .

Answer

200

Solution

Resonant angular frequency: 0= 1 LC

= 1 1.6 40 10-6= 1 64 10-6= 18 10-3

0=125 rad s-1

XL= 0L=125 1.6

XL=200 (equal to XC at resonance; R does not matter)

Answer: 200

JEE Main 2026 (Online) 5th April Evening Shift

Keep practising — Alternating Current

2

An inductor of 10 mH, capacitor of 0.1 μF and a resistor of 100 Ω are connected in series across an a.c. power supply 220 V, 70 Hz. The power factor of the given circuit is 0.5. The difference in the inductive reactance and capacitive reactance is 3 Ω. The value of is .

JEE Main 2026 (Online) 4th April Morning Shift
3

The figure given below shows an LCR series circuit with two switches S1 and S2. When switch S1 is closed keeping S2 open, the phase difference ( ) between the current and source voltage is 30° and phase difference is 60° when S2 is closed keeping S1 open. The value of (3L1-L2) is H. [figure]

  1. 92
  2. 29
  3. 13
  4. 3
JEE Main 2026 (Online) 2nd April Evening Shift
4

The electric current in the circuit is given as i = io(t/T). The r.m.s current for the period t = 0 to t = T is .

  1. io 2
  2. io 3
  3. io
  4. io 6
JEE Main 2026 (Online) 28th January Morning Shift
5

An inductor stores 16 J of magnetic field energy and dissipates 32 W of thermal energy due to its resistance when an a.c. current of 2 A (rms) and frequency 50 Hz flows through it. The ratio of inductive reactance to its resistance is . ( = 3.14)

JEE Main 2026 (Online) 28th January Evening Shift
6

For the series LCR circuit connected with 220 V, 50 Hz a.c. source as shown in the figure, the power factor is 10. The value of is . [figure]

  1. 4
  2. 8
  3. 6
  4. 10
JEE Main 2026 (Online) 24th January Morning Shift
7

Using a variable frequency a.c. voltage source the maximum current measured in the given LCR circuit is 50 mA for V = 5 (100t). The values of L and R are shown in the figure. The capacitance of the capacitor (C) used is . [figure]

JEE Main 2026 (Online) 23rd January Morning Shift
8

A capacitor C is first charged fully with potential difference of V0 and disconnected from the battery. The charged capacitor is connected across an inductor having inductance L. In t s, 25% of the initial energy in the capacitor is transferred to the inductor. The value of t is s.

  1. LC3
  2. LC2
  3. LC2
  4. LC6
JEE Main 2026 (Online) 21st January Evening Shift
9

An ac current is represented as i = 5 2 + 10 (650 t + 6 ) Amp The r.m.s. value of the current is

  1. 10 Amp
  2. 5 2 Amp
  3. 100 Amp
  4. 50 Amp
JEE Main 2025 (Online) 7th April Morning Shift
10

For ac circuit shown in figure, R = 100 k and C = 100 pF and the phase difference between Vin and (VB - VA) is 90 . The input signal frequency is 10x rad/sec, where 'x' is . [figure]

JEE Main 2025 (Online) 7th April Morning Shift
11

An inductor of reactance 100 , a capacitor of reactance 50 , and a resistor of resistance 50 are connected in series with an AC source of 10 V, 50 Hz. Average power dissipated by the circuit is W.

JEE Main 2025 (Online) 7th April Evening Shift

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