In an a.c. circuit with pure capacitance 'C' and a.c. source E = E₀ t , the equation of instantaneous current is given by

Step-by-step solution

The instantaneous voltage across the capacitor is given by E = E₀ t . The charge on the capacitor at any instant is q = CE = CE₀ t . The instantaneous current I is the rate of flow of charge, given by I = dq dt . Differentiating q with respect to t , we get: I = d dt (CE₀ t) = E₀ C t Using the trigonometric identity = ( + 2 ) , the current can be written as: I = E₀ C ( t + 2 ) Answer: I = E₀ C ( t + 2 )