Question

An alternating voltage, $V=60\sin \left(\pi t\right)$ is applied across a $20\Omega$ resistor. What will be the reading of an AC ammeter, connected in series with the resistor?

• A. $3\text{A}$
• B. $\frac{3}{\sqrt{2}}\text{A}$
• C. $1.5\text{A}$
• D. The reading of ammeter will change with time.

Answer 1

The correct option is B $\frac{3}{\sqrt{2}}\text{A}$

An AC ammeter reads the rms value of the AC.

Here,

$V=60\sin \left(\pi t\right)$ and $R=20\Omega$

The current flowing in the circuit is given by,

$i=\frac{V}{R}$

$\Rightarrow i=\frac{60\sin \left(\pi t\right)}{20}=3\sin \left(\pi t\right)$

Comparing the above equation with the standard equation of current, $i.e.i=i_0\sin \omega t$, we get,

$i_0=3\text{A}$

$\therefore$ The rms value of the current is,

$i_{rms}=\frac{i_0}{\sqrt{2}}=\frac{3}{\sqrt{2}}\text{A}$

Hence, option $\left(B\right)$ is the correct answer.