Question

The Electric Current flowing in a circuit is given by
i=2T/3t for some time. The rms Value of current for the
Period t=0 to t=t is,​

Answer 1

The rms value of the current is 2√3/9 A

Explanation:

Given:

The expression for electric current flowing in a circuit

$i=2t/3T$

To find out:

The rms value of the current for a period of t = 0 to t = T

Solution:

We know that rms value of current is given by

$i_{rms}=\sqrt{\bar {i^2}}$

Where

$\bar{i^2}=\frac{\int_0^Ti^2dt}{\int_0^T dt}$

$\implies \bar{i^2}=\frac{\int_0^T(4t^2/9T^2)dt}{T}$

$\implies \bar{i^2}=\frac{4}{9T^3}\int_0^Tt^{2}dt$

$\implies \bar{i^2}=\frac{4}{9T^3}\times\frac{1}{3}t^3\Bigr|_0^T$

$\implies \bar{i^2}=\frac{4}{27T^3}\timesT^3$

$\implies \bar{i^2}=\frac{4}{27}$

Therefore,

$i_{rms}=\sqrt{\frac{4}{27}}$

$\implies i_{rms}=\frac{2}{9}\sqrt{3}$ A

Hope this answer is helpful.

Know More:

Q: The current flowing through a wire depends on  time as I = 3t^2+ 2t + 5. The charge flowing through  the cross-section of the wire in time from t = 0 and  t= 2 sec. is

1) 22 C 2 ) 20 C 3) 18 C 4) 5 C

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