If laplace transform of voltage across capacitor of value 0.5 F is \(\rm V_c(s)=\frac{1}{s^2+1}\), the value of current through capacitor at t = 0⁺ will be:

Question

Question

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RRB JE EE 22 Apr 2025 Shift 1 CBT 2 Official Paper

Answer 1

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

Calculation

Given, C = 0.5F

\(\rm V_c(s)=\frac{1}{s^2+1}=sin( t)\)

\({dV_C\over dt}= cos( t)\)

\(I_C=0.5cos(t)\)

The value of the current through the capacitor at t = 0+ will be:

\(I_C=0.5cos(0)\)

\(I_C=0.5\space A\)