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A capacitor made of two parallel plates each of plate area A and separation d is being charged by an external ac source. Show that the displacement current inside the capacitor is the same as the current charging the capacitor. |
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Answer» SOLUTION :The CAPACITANCE of the parallel plate capacitor `C=(in_0A)/d` EFFECTIVE emf in a purely capacitative circuit driven by an ac voltage V is `V'=V-q/C` `therefore` The circuit EQUATION is `V-q/C=0` or , q=CV `therefore` Charging current , `I=(dq)/(dt)=C(dV)/(dt)=(in_0A)/d (dV)/(dt)` Displacement current , `I_d=in_0(dphi_E)/(dt)=in_0(d)/(dt)(EA)=in_0(d)/(dt)(V/dA)=(in_0A)/(d)(dV)/(dt)` `therefore I_d=I` |
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