What will be the current relationship in time domain for a capacitive circuit?

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RRB JE EE 22 Apr 2025 Shift 2 CBT 2 Official Paper
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  1. \(\rm C\frac{d^2v}{dt^2}\)
  2. \(\rm i(t)=C\frac{dv}{dt}\)
  3. \(\rm i(t)=C\int_0^tv(t)\)
  4. \(\rm i(t)=C\int_0^tv(t)+i(0)\)

Answer (Detailed Solution Below)

Option 2 : \(\rm i(t)=C\frac{dv}{dt}\)
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Detailed Solution

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Concept

The current through a capacitor is given by:

\(I_C=C{dV_C\over dt}\)

where, \({dV_C\over dt}=\) Rate of change of capacitor voltage

The voltage across a capacitor is given by:

\(V_c(t)={1\over C } \int I_c(t) dt\)

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