Question

An AC source is having a voltage given as $E=20sin100t$. This is connected across a resistance given as $20\Omega$. Then what will be the rms value of current in the circuit?
$\begin{aligned} & A.1A \\\ & B.\dfrac{1}{2}A \\\ & C.\sqrt{2}A \\\ & D.2\sqrt{2}A \\\ & E.\dfrac{1}{\sqrt{2}}A \\\ \end{aligned}$

Answer 1

According to the ohm’s law, the current through the circuit can be found by taking the ratio of the potential of the voltage source to the resistance of the resistor connected. Substitute the values in the equation and find the maximum current in the circuit. The root mean square value of the current in the circuit will be equivalent to the $\dfrac{1}{\sqrt{2}}$times the maximum current in the circuit. Substitute the values and arrive at the answer. This will help you in answering this question.

Complete step by step answer:
the AC voltage source is having a voltage mentioned as,
$E=20sin100t$
The resistance connected in the circuit can be written as,
$R=20\Omega$
According to the ohm’s law, the current through the circuit can be found by taking the ratio of the potential of the voltage source to the resistance of the resistor connected. This can be shown in an equation given as,
${{I}_{0}}=\dfrac{{{E}_{0}}}{R}$
Substituting the values in the equation, we can write that,
${{I}_{0}}=\dfrac{20}{20}=1A$
As we all know the root mean square value of the current in the circuit will be equivalent to the $\dfrac{1}{\sqrt{2}}$times the maximum current in the circuit. That is we can write that,
${{I}_{rms}}=\dfrac{{{I}_{0}}}{\sqrt{2}}$
Substituting the value in the equation will give,
${{I}_{rms}}=\dfrac{1}{\sqrt{2}}A$
The value of root mean square current has been obtained as $\dfrac{1}{\sqrt{2}}A$.

So, the correct answer is “Option E”.

Note: The root mean square value is defined as a statistical measure of the magnitude of a changing quantity. We indicate this root mean square to represent the average current or voltage in an AC system. The root mean square value is abbreviated as rms.