Question

An alternating current is flowing in a circuit. The ratio of rms current in the interval of 0 to t0 with the average current in the circuit for the time interval from t / 8 to 3t / 8 (where "t " is time period) is: options 1

Answer 1

Answer:

you give only one option so answer is 1

Answer 2

Answer:

The ratio of rms current in the interval of $0$ to $T$ with the average current in the circuit for the time interval from  $\frac{t}{8}$ to $\frac{3t}{8}$ is $\pi :4$.

Explanation:

Given that $I=I_0sin \omega t$

Now the rms current flow in the circuit is

$I_{rms}^{2}=\frac{\int i^2dt}{\int dt}\\=\frac{\int I_{0}^{2}sin^2\omega t dt}{\int dt}$

After integration and applying limits  $0$ to $T$ the rms current flow in the circuit is

$I_rms=\frac{I_0}{\sqrt{2} }$

Now the average current in the circuit is

$I_{avg}=\frac{\int I dt}{\int dt}$

After integration and applying limits  $\frac{t}{8}$ to $\frac{3t}{8}$  the average current flow in the circuit is

$I_avg=\frac{2\sqrt{2} I_0}{\pi }$

Therefore, the ratio of rms current and the average current is $\bold{\pi :4}$