Question

Find the displacement current through a parallel-plate capacitor. Assume that V is the voltage across the capacitor at any instant. Express your answer in terms of the variables C and dV/dt.

Answer 1

Answer:

displacement current; i_d = C(dV/dt)

Explanation:

Let i_d be the displacement current

Thus,

i_d = ε_o(dΦ/dt)

We know that flux Φ = EA

Thus,

i_d = ε_oA(dE/dt)

We also know that E = V/d

Thus, i_d = ε_oA(d(V/d)/dt)

i_d = ε_o(A/d)(dV/dt)

Now, capacitance has a formula of;

C = ε_o(A/d)

Thus,

i_d = C(dV/dt)