The parallel-plate capacitor shown in Fig. 1 is filled with a lossy dielectric material of...

The parallel-plate capacitor shown in Fig. 1 is filled with a lossy dielectric material of relative permittivity ϵr and conductivity σ. The separation between the plates is d and each plate is of area A. The capacitor is connected to a time-varying voltage source V (t).

(a) Obtain an expression for Ic, the conduction current flowing between the plates inside the capacitor, in terms of the given quantities.

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(b) Obtain an expression for Id, the displacement current flowing inside the capacitor.

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(c) Based on your expressions for parts (a) and (b), give an equivalent-circuit representation for the capacitor.

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(d) Evaluate the values of the circuit elements for A = 2 cm2, d = 0.5 cm, ϵr = 4, σ = 2.5 (S/m), and V(t) = 10 cos(3π × 103t) (V).

Figure 1

Parallel-plate capacitor containing a lossy dielectric material.