Question

The peak value of an alternating current is $5A$ and its frequency is $60Hz$. Find its root mean square value. How much time will the current take to reach the peak value starting from zero?

Answer 1

Hint: The basic equation for alternating current in a in a wire is given as
$I={{I}_{0}}\sin \omega t$
And the rms value is found out by taking the root of the mean of the square of a particular value. These all will help you in solving this question.

Complete step by step answer:
First of all let us discuss the alternating current and root mean square velocity. Alternating current abbreviated as AC is a kind of electric current that periodically changes its direction which is opposite to that of direct current (DC) which only flows in a single direction which will not vary with time. We generally use AC for the working of our television, lights and computers. As the word meaning suggests the current alternates its direction. AC electricity has proven to be a better option supplying electricity than direct current, mainly because the voltages can be transformed.
Here it is given that,
$\begin{align}
  & {{I}_{0}}=5A \\
 & f=60Hz \\
\end{align}$
We know that,
$I={{I}_{0}}\sin \omega t$
Substituting the values in this equation will give,
$I=5\sin 120\pi t$
Therefore the rms value is given as,
${{I}_{0}}=\dfrac{I}{\sqrt{2}}$
That is,
${{I}_{0}}=\dfrac{5}{\sqrt{2}}$
And the time required reach the maximum value from 0 to $\dfrac{T}{4}$$=\dfrac{1}{4f}$
$=\dfrac{1}{4f}=\dfrac{1}{4\times 60}$
$t=\dfrac{1}{240}s$

Therefore the answer is $t=\dfrac{1}{240}s$

Note:
Root Mean Square value of AC is defined as the steady current when passed for a given time through a resistance produces the same amount of heat as the alternating current does in the equal resistance in the similar time. This virtual value or the effective value of alternating current is 0.707 times the topmost value of AC.