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7 June, 03:36

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.

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  1. 7 June, 04:52
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    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)
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