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in Electromagnetic Induction and Alternating Current by (48.5k points)
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Find out the phase relationship between voltage and current in a pure capacitor circuit.

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AC circuit containing only a capacitor: 

Consider a circuit containing a capacitor of capacitance C connected across an alternating voltage source. 

The alternating voltage is given by

Vm sin ωt …… (1) 

Let q be the instantaneous charge on the capacitor. The emf across the capacitor at that instant \(\frac{q}{C}\) is . According to Kirchoff’s loop rule,.

υ = \(\frac{q}{C}\) = 0

⇒ CVm sin ωt 

By the definition of current,

where \(\frac{\frac{V_m}{1}}{\frac{1}{Cω}}\) = Im,

The peak value of the alternating current. From equation (1) and (2), it is clear that current leads the applied voltage by π/2 in a capacitive circuit. The wave diagram for a capacitive circuit also shows that the current leads the applied voltage by 90°.

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