A parallel plate capacitor having plate area ‘A’ and plate separation ‘d’ is joined to a battery of emf ‘V’ and internal resistance ‘R’ at $$t=0$$ . Consider a plane surface of area $$A/3$$, parallel to the plates and situated symmetrically between them. Find the displacement current through this surface as a function of time. [ The charge on the capacitor at time ‘t’ is given by $$q=CV1$$−etτwhere τ$$=CR$$ ]

Question

A parallel plate capacitor having plate area ‘A’ and plate separation ‘d’ is joined to a battery of emf ‘V’ and internal resistance ‘R’ at  $$t=0$$ . Consider a plane surface of area $$A/3$$,  parallel to the plates and situated symmetrically between them. Find the displacement current through this surface as a function of time. [ The charge on the capacitor at time ‘t’ is given by $$q=CV1$$−etτwhere  τ$$=CR$$ ]

Infinity Learn · Accepted Answer

Surface charge density,  σ$$=qA=CVA1$$−e−tτ Electric field $$b/w$$ the plates of capacitor, $$E=$$σ∈$$0=CV$$∈$$0A1$$−e−tτ Electric flux from the given area, ϕ$$E=EA3=CV3$$∈$$01$$−e−tτ Displacement current, $$id=$$∈$$0d$$ϕ$$Edt=$$∈$$0ddtCV3$$∈$$01$$−e−tτ$$=CV3$$τe−tτ ⇒$$id=V3Re$$−tCR ⇒$$id=V3Re$$−td∈$$0AR$$

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