Now consider an ac circuit consisting of a resistor of resistance R and a capacitor of capacitance C in series with’ an ac source supposes in phasor diagram current is taken along positive x-direction.
Then VR is along positive x-direction but VC is along negative y-direction as potential difference across a capacitor in ac lags in phase by 90° with the current in the circuit
So we can write.
and the potential difference lags the current by an angle,
Illustration 3 : An a.c. source of angular frequency is ,fed across a resistor R and a capacitor C in series. The current registered is l. If now the frequency of the source is changed to w/3 (but maintaining the same voltage), the current in the circuit is found to be halved. Calculate the ratio of reactance of resistance at the original frequency.
Solution: At angular frequency , the current in R-C circuit is given by
When frequency is changed to the current is halved Thus
From equation (i) and (ii),
Solving this equation,
Hence, the ratio of reactance to resistor is