A parallel plate capacitor of capacitance C is connected to a time-varying voltage source given by V(t) = V₀ ^2( t) . The maximum value of the displacement current between the plates of the capacitor is:

Step-by-step solution

The displacement current I_d between the plates of a capacitor is equal to the conduction current, which is given by the rate of change of charge on the capacitor. The charge on the capacitor at any time t is: q(t) = C V(t) = C V₀ ^2( t) Differentiating with respect to time t to find the displacement current: I_d = dq dt = d dt (C V₀ ^2( t)) I_d = C V₀ (2 ( t) ( t)) Using the trigonometric identity 2 ( t) ( t) = (2 t) : I_d = C V₀ (2 t) The maximum value of the displacement current occurs when (2 t) = 1 . (I_d)_ =