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.

Explanation

C = ?
`R= 10Omega`
`L= 40 mH = 40 xx 10^(-3)H`
`v= 60 Hz`
Current is in phase with voltage at resonance i.e., when `X_L = X_C`
`implies 2pivL =1/(2pivC)`
`C =1/(4pi^2v^2L)`
`1/(4xx(3.14)^2xx(60)^2 xx40xx10^(-3))`
`1000/(4xx9.8596xx3600xx40)`
`=1/(16xx36xx9.8596)`
`C = 0.000176F`
`C = 1.76xx10^(-4)F`