Question

The average value of current for the current shown for time period 0 to is:

A. $\dfrac{{{I_0}}}{{\sqrt 2 }}$
B. $\dfrac{{{I_0}}}{2}$
C. $\dfrac{{{I_0}}}{{\sqrt 3 }}$
D. $\dfrac{{2{I_0}}}{{\sqrt 3 }}$

Answer 1

Hint: Average current for AC is defined as that DC current which when transferred across the circuit will produce the same amount of charge that was produced by the earlier for the same duration of time.

Complete Step by Step Answer:
Average current depicts to the mean of every instantaneous current unit from zero to the peak and back again in a sinusoidal wave. Alternating or A-C current is depicted by a sinusoidal wave.
 Express the relation to find the average value of the current in current time curve:
 ${I_{avg}} = \dfrac{A}{{{T_c}}}$
 Here, A is the area and Tc is the total time interval.
 Substitute $\dfrac{1}{2}{I_0} \times \dfrac{T}{2}$ for A and T/2 for Tc to find the value of ${I_{avg}}.
 $\begin{array}{l}
{I_{avg}} = \dfrac{{\dfrac{1}{2}{I_0} \times \dfrac{T}{2}}}{{\dfrac{T}{2}}}\\
{I_{avg}} = \dfrac{{{I_0}}}{2}
\end{array}
Therefore, the correct option is (B).

Note: It is well understood that if alternating current at a circuit flows for T sec and charge q is moved across any location of circuit in this time T through this AC current, then the equal amount charge q should also be transferred by its avg. current in the same duration.