Question

An EMF 220 volt is applied to a circuit containing register a having resistance 160ohm, and capacitor in series. the current is found to lead voltage by an angle theta = tan^-1(3/4). Calculate Capacitive reactance, impedence, current flow in circuit?

Answer 1

For an R-C circuit, if `V=V_o sin omegat`

then `I=I_o sin (omegat + theta)` where, current leads voltage by `theta`

and,we know, from phasor diagram `tan theta=(X_c)/R` where, `X_c` is the capacitive reactance and `R` is the resistance.

Given, `theta=tan^-1(3/4)`

So,`tan theta=3/4=(X_c)/160`

or, `X_c=120 Omega`

Impedenace i.e `Z` is `sqrt(R^2 +X_c ^2)=200 Omega`

Current flowing in the circuit is `(V_o)/Z=220/200=1.1 A`