Question

Consider the circuit shown in figure. If the frequency of the source is 50 Hz, then a value of $t_0$ which results in a transient free response is

• A. 0 ms
• B. 1.78 ms
• C. 2.71 ms
• D. 2.91 ms

Answer 1

The correct option is B 1.78 ms

For transient free response,

$tan\left(\omega t_0\right)=\frac{\omega L}{R}$

$tan(2\pi \times 50\times t_0)=\frac{2\pi \times 50\times 0.01}{5}$

$2\pi \times 50\times t_0=ta{n}^{-1}\left(\frac{\pi }{5}\right)$

= ${32.14}^0=0.561rad$

$t_0=\frac{0.561}{100\pi }=1.786ms$