Question

In the circuit shown, the voltage across capacitor is

• A. \(200\,\mu s\)
• B. \(100\,\mu s\)
• C. \(-100\,\mu s\)
• D. \(-200\,\mu s\)

Hint:

Time constant \( \tau = RC \).

Answer 1

The Correct Option is B

Step 1: Identify the RC time constant formula.
For any RC circuit, the time constant is $\tau = R \times C$. This is the time it takes the capacitor voltage to rise to about $63\%$ of its final value during charging, or to fall to $37\%$ during discharging.

Step 2: Substitute the given values.
With $R = 5\,k\Omega = 5 \times 10^3\,\Omega$ and $C = 20\,nF = 20 \times 10^{-9}\,F$: $\tau = (5 \times 10^3) \times (20 \times 10^{-9}) = 100 \times 10^{-6}\,s$.

Step 3: Express in microseconds.
$\tau = 100 \times 10^{-6}\,s = 100\,\mu s$. \[ \boxed{100\,\mu s} \]