Question

An AC source is \(120\) V - \(60\) Hz. The value of voltage after \(\frac{1}{720}\) s from start will be \(\left(\sin 30^{\circ }=\frac{1}{2}\right)\)

• A. \(20.2V\)
• B. \(42.4V\)
• C. \(84.8V\)
• D. \(106.9V\)

Hint:

The quoted 120 V is the rms value, so the peak is 120 times root 2, then evaluate V equal to V0 sin omega t.

Answer 1

The Correct Option is C

Step 1: Equation of the source
$V=120\sqrt{2}\sin(2\pi\times60\,t)$.

Step 2: Substitute t
$2\pi\times60\times\dfrac{1}{720}=\dfrac{\pi}{6}$, so $\sin\dfrac{\pi}{6}=\dfrac{1}{2}$.

Step 3: Evaluate
$V=60\sqrt{2}\approx84.8$ V, option (C).

Final Answer:
The voltage is about 84.8 V. \[ \boxed{\text{(C) }84.8\,V} \]