Question

Derive the expression for current when AC voltage applied to a capacitor. mention the expression for capacitive reactance. 

Answer 1

Consider a capacitor of capacitance C is connected across an AC source, 

Let v = v_msin ωt --------(1), here v - the source voltage, v_m – peak voltage , ω - angular frequency of AC. 

The p.d. across the capacitor at any instant of time is v = q/C 

According to Kirchoff’s loop rule, v_m sin ωt - q/C = 0 

Let ωv_mC = i_m be the amplitude of the current, then i = i_m cos ωt 

Capacitive Reactance : X_C : 

Capacitive reactance is given by = X_C = 1/ωC = 1/2πνC = 1/2πfC 

The SI unit of X_C is ohm (Ω) 

Defination of X_C :