A series circuit contains a resistor of `20 Omega`, a capacitor and an ammeter of negligible resistance. It is connected to a source of 200 V, 50 Hz. If the reading of ammeter is 2.5 A, calculate the reactance of the capacitor.

Explanation

Here `R = 20 Omega, E_(rms) = 200 V, v = 50 Hz, I_(rms) = 2.5 A`
The circuit is CR circuit.
Impedance of circuit.
`Z_(CR) = (E_(rms))/(I_(rms)) = (200)/(2.5) = 80 Omega`
But, `Z_(CR) = sqrt(R^(2) + X_(C)^(2))`
or `X_(C)^(2) = Z_(CR)^(2) - R^(2)`
or `X_(C)^(2) = sqrt(Z_(CR)^(2) - R^(2)) = sqrt((80)^(2) - (20)^(2)) = 77.46` ohm