Question

The RMS value of current in an AC circuit is 10 A. What is the peak current?
A. 14.1A
B. 35.2A
C. 58.9A
D. 23.5A

Answer 1

We have already learnt the derivation for relation between peak value of AC and RMS value of AC in chapter Alternating Current of unit 4 in Class 12. Since, we have already given the RMS value of current. Simply, substitute the numerical values given in below given mathematical formula for finding the asked value.

Complete step by step answer:
Given that, the RMS value of current in an AC circuit is 10 A.Now, RMS value i.e., Root Mean Square value which is also known as Effective value of Alternating Current or Virtual value of Alternating Current. We may define it as that value of steady Current (or Direct Current) which would generate the same amount of heat as it generated by alternating Current in the same circuit for the full time period.

In simple words, we can say that the amount of heat produced due to alternating current in a circuit A then the same amount of heat should be produced in an another circuit B due to Direct current and that value of direct current is known as the Root Mean Square value of Alternating current. It is represented as ${{\text{I}}_\nu }$ or ${{\text{I}}_{effective}}$ or${{\text{I}}_{RMS}}$.Through derivation, we concluded with the mathematical expression as:
${{\text{I}}_{RMS}} = \dfrac{{{I_0}}}{{\sqrt 2 }}$ ……………………………………… Eq.1
Where, ${{\text{I}}_0}$= peak current or maximum current.
${{\text{I}}_{RMS}}$= Root Mean Square value of Alternating current.
Substituting value of $\dfrac{1}{{\sqrt 2 }} = 0.7071$in above formula, we get
${{\text{I}}_{RMS}} = 0.707{{\text{I}}_0}$……………………………. Eq.2
We need to find the value of peak current. Peak current is also called maximum current.
Substitute the numerical value of ${{\text{I}}_{RMS}}$from the question into either Eq.1 or Eq.2,

$$10 = 0.707{{\text{I}}_0} \\\ \Rightarrow \dfrac{{10}}{{0.707}} = {{\text{I}}_0} \\\ \Rightarrow 14.144 = {{\text{I}}_0} \\\$$

$\therefore{{\text{I}}_0} = 14.144$ approx. ${{\text{I}}_0} = 14.1$ A
The peak value of alternating current is 14.1 Ampere in a circuit where RMS value of current is 10 Ampere.

So, option A is correct.

Note: Always write the units of physical quantity in the end of solution. RMS value for any physical quantity can never be negative. Also, in RMS value we considered the full cycle of alternating current instead of half cycle which we consider in Average value of AC.Go through from the derivation for more clarity.