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For the circuit diagram shown below, calculate the voltage across capacitor V(t) at t = 160 μs?

For the circuit diagram shown below, calculate the voltage across capacitor V(t) at t = 160 μs? Correct Answer 18.4 V

Concept:

The voltage across the capacitor Vc(t) is given by the following transient equation.

Vc(t) = Vc(∞) + (Vc(0+) – Vc(∞)) e-t/τ

Calculation:

At t = 0-, the capacitor acts as an open circuit. The voltage across the capacitor is,

Vc(0-) = 50 V

At t = 0+, as the capacitor does not allow the sudden change in voltage,

Vc(0-) = Vc(0+) = 50 V

At t = ∞, as there is no source, the voltage across the capacitor is zero.

Vc(∞) = 0 V

Time constant τ = RC = 80 × 2 μ = 160 μ

Now, Vc(t) = V­c(∞) + (Vc(0+) – Vc(∞))e-t/τ

Vc (160 × 10-6) = 50 e-160 μ/160 μ

= 50 e-1

Voltage across capacitor Vc(t) = 18.39 V

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