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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 :

  1. Id = V0 ωCsinωt
  2. Id = V0 ωCcosωt
  3. Id = \(\frac{{{V_0}}}{{\omega C}}\) cosωt
  4. Id = \(\frac{{{V_0}}}{{\omega C}}\) sinωt

Answer (Detailed Solution Below)

Option 2 : Id = V0 ωCcosωt
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Detailed Solution

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Given V = V0sinωt      --- (1) 

Now displacement current I d is given by

\({I_d} = C\frac{{dV}}{{dt}}\)

\({I_d} = C\frac{d}{{dt}}\)(V0 sinω t)

= C (V0 ω) cosωt

Id = V0 ωCcosωt

Hence, Option 2) is correct choice.

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