Question

A voltmeter connected across a 60Hz ac source reads 240V. Write down the expression of the instantaneous voltage as a function of time.

Answer 1

The voltage varies sinusoidally, so it'll be a sine function of time. The voltmeter reads the rms voltage, which is 1/sqrt(2) of the peak voltage. The angular frequency of the supply is 2(pi)f, so...
\[V(t)=240\sqrt{2}\sin(120\pi t)\]