1.

A capacitor, made of two parallel plates each of plate area A and separation d, is being charged by an external ac socurce. Show that the displacement current inside the same as the current charging the capacitor.

Answer» Let the alternating emf charging the plates of the capacitor `epsilon=epsilon_(0) sin omegat.`
Charge on capacitor
`q=C_(epsilon)=C_(epsilon_(0))sin omegat`
Let Instantaneous current be I
`So," "I=(dq)/(dt)=(d)/(dt)C_(epsilon_(0)) sin omega t`
`=C_(epsilon_(0))omega cos t`
`=I_(0) cos omega t`
`"where, "I_(0)=C_(epsilon_(0))omega`
`I_(d)=in_(0)(dphi_(E))/(dt){phi_(E)=EA.`
`I_(d)=in_(0) A(DE)/(dt){E=(sigma)/(in_(0))=(q)/(A_(in_(0)))`
`I_(d)=in_(0)A(d)/(dt)((q)/(A_(in_(0))))`
`I_(d)=(d)/(dt)C_(epsilon_(0))sin omega t = C_(epsilon_(0))omega cos omegat= I_(0) cos omega t`
Hence, conduction current is equal to the displacement current.


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