Effective or RMS Value of AC

Correct: Average value of a.c. is $\frac{I_0}{\sqrt{2}}$.

Correct: The r.m.s value of an a.c. is $\frac{{\mathrm{I}}_0}{2}$.

What is alternating current? Prove the following for a.c

(i) ${\mathrm{I}}_{\mathrm{eff}}=\raisebox{1ex}{${\mathrm{I}}_0$}\!\left/ \!\raisebox{-1ex}{$\sqrt{2}$}\right.$

Write down the equation that represents a sinusoidal a.c. Obtained expression for its mean value and rms value over one cycle in terms of the peak current. Why is a.c considered to be more dangerous than d.c?

Differentiate between direct current and alternating current. Obtained an expression for the rms value of the latter i.e., a.c over cycle. What is the difficulty in using the average value of a.c?

A current is made of a $3\mathrm{amp}$ d.c. component and an a.c component given by $I=4\sin wt$ amp. Find an expression for the resultant current and calculate its effective value. [Hint: $I=I_{d.c}+I_{a.c}$ find the square of $I$ and hence obtained $I_{rms}$].

If the electric current in a circuit is given by $I=I_0\left(\raisebox{1ex}{$t$}\!\left/ \!\raisebox{-1ex}{$\tau $}\right.\right)$ for some time, find the RMS current for the period from $t=0 \mathrm{to} t=\tau$.

A $60\mathrm{Hz}$ a.c. circuit has a voltage of $120$ volts and current of $6 \mathrm{amp}$. (effective values). Find the maximum values of these quantities. What is the instantaneous value of the voltage $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$720$}\right. \sec$. after the voltage has zero value?

Alternating current in a circuit is given by $I=50\sin 400\mathrm{\pi t}$. Find the frequency and the RMS value of the current.

Write down an equation representing alternating current and explain the symbols used in it.

Differentiate between RMS value and average value of AC over a cycle.

Explain what is RMS value of AC.

Define RMS value of AC.