InterviewSolution
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InterviewSolution
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Prove that the total current which is the sum of conduction current and displacement current is always continuous and any loss in conduction current (I_C) appears as displacement current (I_D). |
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Answer» Solution :Consider a volume V in a medium through which currents are flowing. Let `I_c` be the conduction current entering the volume V and `I_c'` be the conduction current leaving the volume V. Then total charges entering and leaving the volume in time dt will be `I_c` and `I_c'`dt. Therefore, the CHARGE ACCUMULATED inside the volume V during time dt is GIVEN by dq(inside V)=`I_cdt-I_c'dt` or `(dq)/(dt)=I_c-I_c'....(i)` From Gauss's Theoram in electrostatics, we have `phi_E=ointvecE.vec(DS)=q/(in_0) ("inside") or in_0 phi_E=q` or `I_d=in_0 (dphi_E)/(dt)=(d (in_0phi_E))/(dt)=(dq)/(dt) ......(ii)` From (i) and (ii), `I_c-I_c'=I_d or I_c=I_d+I_c'` Thus we conclude that the loss of conduction current `(=I_c-I_c')` appears as the DISPLACEMENT current `(I_d)` and conduction current plus displacement current remains constant i.e., `I_c'+I_d`= a constant. |
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