A capacitor with capacitance C whose interelectrode space is filled up with poorly conducting medium with active resistance R is connected to a source of alternating voltage v = V M cos ω t. Find the time dependence of the steady-state current flowing in lead wires. The resistance of the wires is to be neglected.
Text Solution
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Sol. If the space between electrodes is filled with poorly conducting material, then the system behaves as a parallel combination of resistance and capacitor, (shown in figure.)
Here X C = 
∴ 
= 
+ 
(–j) (in complex representation)
or 
= 
– 
or 
= 
+ ω Cj
or 
= 
∴ Z = 
∴ Ζ = 
∴ I = 
= 
I = I M cos( ω t + φ )
∴ Ι Μ = 
= 
tan φ = 
= 
∴ tan φ = ω RC
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