Chapter 6, Problem 16P

The parallel-plate capacitor shown in Fig. P6.16 is filled with a lossy dielectric material of relative permittivity ϵ_r 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).

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

Figure P6.16 Parallel-plate capacitor containing a lossy dielectric material (Problem 6.16).

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

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

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