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An inductance L , a capacitor of 20muF a...

An inductance L , a capacitor of `20mu`F and a resistor of `10Omega` are connected in series with an AC source of frequency 50 Hz . If the current is in phase with the voltage, then the inductance of the inductor is

A

2.00 H

B

0.51 H

C

1.5 H

D

0.99 H

Text Solution

Verified by Experts

The correct Answer is:
B
In an L-C-R circuit , the current and the voltage are in phase (`phi` = 0), when
`tan phi` = `omegaL - 1/omegaC / R` or `omegaL = 1/omegaC`
`L = 1 / omega^(2)`C
Here, `omega = 2pif = 2 xx 3.14 xx 50 s^(-1) = 314 s^(-1)`
and C = `20muF = 20 xx 10^(-6)` F
`therefore L = 1 / (314 s^(-1)^(2) xx (20 xx 10^(-6) F )` = 0.51 H
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