Now consider an ac circuit consisting of a resistor of resistance R, a capacitor of capacitance C and an inductor of inductance L, in series with an ac source generator. Suppose in a phasor diagram, current is taken along positive x-direction. Then VR is along positive x-direction. VL. along positive y- direction and Vc along negative y-direction, as potential difference across an inductor leads the current by 90° in phase while that across a capacitor, lags it in phase by 90°.
Here impendence is,
The modulus of impedance is,
Difference leads the current by an angle.
The steady current in the circuit is given by
It depends on angular frequency ω of ac source and it wi1l be maximum
when ωL-1/ωC=0
If the resistance R in the LCR circute is zero,the peak current at resonance is
It means there can be a finite current in pure LC circute even without any applied emf, This current in the circuit is at frequency,
Illustration 4: A resistance R, and inductance L and a capacitor C all are connected in series with an a.c. supply. The resistance of R is I6 ohm and for a given frequency , the inductivity reactance of L is 24 ohm and .capacitive reactance of C 12 ohm .If the current in the circuit is 5 amp, find
(a) the potential difference across R,L and C (b) the impedance of the circuit
(c) the voltage of a.c supply (d) phase angle
Solution: (a) Potential difference across resistance