91Ó°ÊÓ

The charge q on a capacitor in a simple a-c circuit varies with time according to the equation $q=3\sin (120\mathrm{Ï€}t+\mathrm{Ï€}/4)$.

Time Period (T): The length of time it takes for a motion to repeat itself. Thus, a time period is measured in seconds.

Frequency (f): It is determined by counting how many times a motion is repeated in a second. Hz is the symbol for frequency (Hertz).

Frequency is related to Time period as $\mathit{f}\mathbf{=}\frac{\mathbf{1}}{\mathbf{T}}$.

Following is the variation of charge:

$q=3\sin (120\mathrm{Ï€}t+\mathrm{Ï€}/4)$

So, amplitude = 3.

The distance functions of the form$A\sin \left(\mathrm{Ó\neg }t-\mathrm{Ï•}\right)$.

So, $\mathrm{Ó\neg }=120\mathrm{Ï€}$.

Then, obtain values:

Period$=\frac{2\mathrm{Ï€}}{\mathrm{Ó\neg }}$

Period $=\frac{2\mathrm{Ï€}}{120\mathrm{Ï€}}$

Period$=\frac{1}{60}$

The frequency is defined as the inverse of the period

So, obtain:

$Frequency=\frac{1}{period}$

Frequency = 60

Hence, l is a sinusoidal function of t.