In an AC circuit, the current is $I=100\,\sin (5t)$ A. The value of $I_{rms}$ is

Question

In an a.c. circuit, voltage and current are given by: \[ V = 100 \sin(100t) \, \text{V} \quad \text{and} \quad I = 100 \sin\left(100t + \frac{\pi}{3}\right) \, \text{mA}. \] The average power dissipated in one cycle is:

Answer 1

Step 1: Formula-first approach
$I_{rms}=0.707\,I_0$.

Step 2: Compute
$\dfrac{100}{\sqrt{2}}=50\sqrt{2}\approx70.7$ A.

Step 3: Why the other options fail
Zero is the average over a cycle, not the rms value.

Final Answer:
The rms current is 50 root 2 ampere. \[ \boxed{\text{(B) }50\sqrt{2}\ \text{A}} \]

In an AC circuit, the current is \(I=100\,\sin (5t)\) A. The value of \(I_{rms}\) is

Show Hint

The Correct Option is B

Solution and Explanation

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