sin ω t passing through a resistor R , the average power loss P (averaged over a cycle) due to joule heating is ( / ) i m R . To express it in the same form as the dc power ( P = I R ), a special value of current is used. It is called root mean square (rms) current and is donoted by I : . i I i Similarly, the rms voltage is defined by .
v v We have P = IV = I R . An ac voltage v = v m sin ω t applied to a pure inductor L , drives a current in the inductor i = i m sin ( ω t – π / ), where i m = v m / X L . X L = ω L is called inductive reactance . The current in the inductor lags the voltage by π / .
The average power supplied to an inductor over one complete cycle is zero. . An ac voltage v = v m sin ω t applied to a capacitor drives a current in the capacitor: i = i m sin ( ω t + π / ). Here, , v i X X is called capacitive reactance .
The current through the capacitor is π / ahead of the applied voltage. As in the case of inductor, the average power supplied to a capacitor over one complete cycle is zero. . For a series RLC circuit driven by voltage v = v m sin ω t , the current is given by i = i m sin ( ω t + φ ) where ( L v i X X and tan L X X φ ( L Z X X is called the impedance of the circuit.