616 the parallel plate capacitor shown in fig p616 is filled with a lo

Question

6.16 The parallel-plate capacitor shown in Fig. P6.16 is filled with a lossy dielectric material of relative permittivity & and conductivity o. 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. (b) Obtain an expression for Ia, the displacement currentflowing 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, &= 4, 0 = 2.5 (S/m), and V(t)=10 \cos \left(3 \pi \times 10^{3} t\right)