Question

The relation between an ac voltage source and time in SI units is V = 120 sin$(100\ \pi t)\cos(100\pi t)\text{ V}.$ The value of peak voltage and frequency will be respectively

• A. 120 V and 100 Hz
• B. $\frac{\text{120}}{\sqrt{2}}\text{ Vand 100 Hz}$
• C. 60 V and 200 Hz
• D. 60 V and 100 Hz

Answer 1

Answer: (D)

60 V and 100 Hz

Answer 2

: $V = 120\sin(100\pi t)\cos(100\pi t)V$

$= 60\sin(200\pi t)$

$(\because\sin 2\theta = 2\sin\theta\cos\theta$)

Compare it with standard equation

$V = V_{0}\sin\omega t$We get

$V_{0} = 60V$ and ,$\omega = 200\pi$ or $2\pi\upsilon = 200\pi$ or $\upsilon = 100Hz$