A parallel plate capacitor of plate area A each and seperation d, is being charged by an ac source Show that the displacement current inside the capacitor is the same as the current charging the capacitor(CBSE 2019) .
Answer:
`I_d`=`epsilon_0frac{dphi_E}{dt}`
`I_d`=`epsilon_0frac{d(E.A)}{dt}`--------------(1)
Q=CV
V=Ed
`therefore`E.A `=frac{(Q A)}{Cd}`
C=`epsilon_0frac{A}{d}`
`therefore`E.A `=frac{Q}{epsilon_0}`(also by Gauss's Theorem)
substituting in (1) `I_d`=`frac{dQ}{dt}`
ie `I_d`= I
Answer:
`I_d`=`epsilon_0frac{dphi_E}{dt}`
`I_d`=`epsilon_0frac{d(E.A)}{dt}`--------------(1)
Q=CV
V=Ed
`therefore`E.A `=frac{(Q A)}{Cd}`
C=`epsilon_0frac{A}{d}`
`therefore`E.A `=frac{Q}{epsilon_0}`(also by Gauss's Theorem)
substituting in (1) `I_d`=`frac{dQ}{dt}`
ie `I_d`= I
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