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An LCR series circuit consists of a resi...

An LCR series circuit consists of a resistance of a `10 Omega` a capacitance of reactance `60 Omega` and an inductor coil The circuit is found to resonate when put across a `300 V ,100 ` Hz supply The inductance of the coil is `(taken pi =3)` .

A

0.1 H

B

0.01 H

C

0.2 H

D

0.02 H

Text Solution

Verified by Experts

The correct Answer is:
A
Angular velocity,
`omega_o = 2pinu= 2pi xx 100`
`omega_o = 2 xx 3 xx 100`
= `600 rad s^(-1)` [since`pi` = 3]
Further , `omega_o = 1 / sqrt LC` …..(i)
Also, `X_C = 1 / COmega_o = 60 Omega`
`implies C = 1 / omega_(o) xx 60 = 1 / 600 xx 60impliesC = 1 / 36 xx 10^(3)` F
so, put values in Eq(i), we get
`600 = 1 / sqrt(L(1/36 xx 10^(3)))`
`implies 36 x 10^(4) = 36 xx 10^(3) / L implies 36 xx 10^(3) / 36 xx 10^(4) = 1/10` = 0.1 H
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