A capacitor of capacitance 'C', is connected across an ac source of voltage V, given by V = V 0 sin ω t The displacement current between the plates of the capacitor, would then be given by:

Question

A capacitor of capacitance 'C', is connected across an ac source of voltage V, given by V = V 0 sin ω t The displacement current between the plates of the capacitor, would then be given by: (A) I d = V 0 ω C cos ω t (B) Id=(V0/ω C) cos ω t (C) I d =( V 0/ω C ) sin ω t (D) I d = V 0 ω C sin ω t

Tardigrade Admin · Accepted Answer

Id=Vo ω C cos ω t Given V=V0 sin ω t Now, displacement current id is given by, Id=C (d V/d t)=C (d/d t)(V0 sin ω t) = C ( V 0 ω) cos ω t =V0 ω C cos ω t

Q. A capacitor of capacitance $^{'} C^{'}$ , is connected across an ac source of voltage $V$ , given by $V = V_{0} sin ω t$
The displacement current between the plates of the capacitor, would then be given by:

$I_{d} = V_{0} ω C cos ω t$

$I_{d} = \frac{V _{0}}{ω C} cos ω t$

$I_{d} = \frac{V _{0}}{ω C} sin ω t$

$I_{d} = V_{0} ω C sin ω t$

$I_{d} = V_{o} ω C cos ω t$
Given $V = V_{0} sin ω t$
Now, displacement current $i_{d}$ is given by,
$I_{d} = C \frac{d V}{d t} = C \frac{d}{d t} (V_{0} sin ω t)$
$= C (V_{0} ω) cos ω t$
$= V_{0} ω C cos ω t$

Q. A capacitor of capacitance ′C′, is connected across an ac source of voltage V, given by V=V0​sinωt The displacement current between the plates of the capacitor, would then be given by:

Id​=V0​ωCcosωt

Id​=ωCV0​​cosωt

Id​=ωCV0​​sinωt

Id​=V0​ωCsinωt