JEE Main · 2021 · 27 Jul 2021 · Shift 2 · Alternating Current

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100Ω

resistance, a

0.1 μ F

capacitor and an inductor are connected in series across a 250 V supply at variable frequency. Calculate the value if inductance of inductor at which resonance will occur. Given that the resonant frequency is 60 Hz.

(A) $7.03 \times 1 0^{- 5} H$
(B)70.3 H✓ Correct
(C)70.3 mH
(D)0.70 H

Answer: (B)

Solution

At resonance the inductive and capacitive reactances cancel, so

ω^{2} = \frac{1}{L C}

and

L = \frac{1}{4 π ^{2} f ^{2} C} = \frac{1}{4 π ^{2} \times ( 60 ) ^{2} \times 1 0 ^{- 7}}

L = \frac{1 0 ^{7}}{4 \times 9.87 \times 3600} = 70.3 H

The inductance at which resonance occurs is

70.3

JEE Main · 2021 · 27 Jul 2021 · Shift 2 · Single correct option

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