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A capacitor, a 15Omega resistor and 101....

A capacitor, a `15Omega` resistor and 101.5 mH inductor are placed in series with 50 Hz. AC source. Calculate the capacitance of the capacitor, if the current is observed in phase with the voltage.

Text Solution

Verified by Experts

The correct Answer is:
99.7
We are given that, `R = 15Omega`
`L=101.5mH = 101.5xx10^(-3)H, v = 50 Hz`
For an RLC series ac circuit, `tan phi= (X_L-X_C)/R`
If current is in phase with the voltage, `phi = 0^@`
i.e., `tan phi` = 0 or `((X_L- X_C))/R = 0`
or `X_L – X_C = 0` or `X_L= X_C`
or `omegat = 1/(omegaC)`
`C=1/(omega^2L)=1/(4pi^2 v^2L)`
`=1/(4xx(3.14)^2 xx(50)^2 (101.5xx10^(-3)))`
`=99.7muF`
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