Question

An alternating current is represented by the equation, $\mathrm{i}=100 \sqrt{2} \sin (100 \pi \mathrm{t})$ ampere. The RMS value of current and the frequency of the given alternating current are

• A. $100 \sqrt{2} \mathrm{~A}, 100 \mathrm{~Hz}$
• B. $\frac{100}{\sqrt{2}} \mathrm{~A}, 100 \mathrm{~Hz}$
• C. $100 \mathrm{~A}, 50 \mathrm{~Hz}$
• D. $50 \sqrt{2} \mathrm{~A}, 50 \mathrm{~Hz}$

Hint:

The RMS value of an alternating current is given by the peak value divided by $\sqrt{2}$.

Answer 1

The Correct Option is C

1. Root Mean Square (RMS) value of current: \[ i_{\text{rms}} = \frac{i_0}{\sqrt{2}} = 100 \mathrm{~A} \]
2. Frequency of the current: \[ f = \frac{\omega}{2\pi} = \frac{100\pi}{2\pi} = 50 \mathrm{~Hz} \] Therefore, the correct answer is (3) $100 \mathrm{~A}, 50 \mathrm{~Hz}$.