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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 omegat. Find the time dependence of the steady - state current flowing in lead wires. The resistance of the wires is to be neglected. |
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Answer» Solution :We use the complex voltage `V=V_(m) e^( i omegat). ` Then the voltage across the capacitor is `(I-I^('))(1)/( iomegaC)` and that across the resistance `RI^(') ` and both equal `V`. Thus `I^(')=(V_(m))/( R) e^(I omegat), I-I^(') =iomegaCV_(m)e^(iomegat)` Hence `I=(V_(m))/( R)(1+ iomegaRC) e^(iomegat)` The actual voltage is OBTAINED by taking the real part. Then `I=(V_(m))/(F) sqrt(1+ ( omegaRC)^(2))cos ( omegat+ varphi)` Where ` tan varphi= omega RC` Note `rarr A` condenser with poorly conducting material `(` dielectric of high resistance `)` be the plates is equivalen to an an ideal condenser with a high resistance JOINED in `p` between its plates. 
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