JEE Main · 2022 · 29 Jun 2022 · Shift 2 · Alternating Current

An inductor of 0.5 mH, a capacitor of

200 μ F

and a resistor of

2Ω

are connected in series with a 220 V ac source. If the current is in phase with the emf, the frequency of ac source will be ______

\times 1 0^{2} Hz

Answer: 5

Solution

When the current is in phase with the emf in an LCR circuit, the circuit is at resonance. The resonant frequency is:

f = \frac{1}{2 π L C}

Substituting the given values:

f = \frac{1}{2 π 0.5 \times 1 0 ^{- 3} \times 2 \times 1 0 ^{- 4}} = \frac{1}{2 π 1 0 ^{- 7}} = \frac{1}{2 π \times 1 0 ^{- 3.5}}

f = \frac{10}{2 π} \times 1 0^{3} \approx \frac{3.162}{6.283} \times 1000 \approx 500 Hz

Therefore, the frequency is

5 \times 1 0^{2}

Hz, giving

x = 5

JEE Main · 2022 · 29 Jun 2022 · Shift 2 · Integer answer