A transmitting station releases waves of wavelength 960 m . A capacitor of $2.56 \mu \mathrm{~F}$ is used in the resonant circuit. The self inductance of coil necessary for resonance is \_\_\_\_ $\times 10^{-8} \mathrm{H}$.

JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Alternating Current

A transmitting station releases waves of wavelength 960 m . A capacitor of

2.56 μ F

is used in the resonant circuit. The self inductance of coil necessary for resonance is ____

\times 1 0^{- 8} H

Answer: 10

The circuit has to resonate at the frequency of the wave being transmitted:

f = \frac{c}{λ} = \frac{3 \times 1 0 ^{8}}{960} = 3.125 \times 1 0^{5} Hz

At resonance

f = \frac{1}{2 π L C}

, which rearranges to

L = \frac{1}{4 π ^{2} f ^{2} C} = \frac{1}{4 π ^{2} ( 3.125 \times 1 0 ^{5} ) ^{2} ( 2.56 \times 1 0 ^{- 6} )} = 1.01 \times 1 0^{- 7} H

Written in the units asked for, the self inductance of the coil is

10 \times 1 0^{- 8}

JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Integer answer