Question

A complex current wave is given by \[i=\left( 5+5sin100\text{ }\pi t \right)A\]. Its average value over one time period is given as
a. \[10A\]
b. \[5A\]
c. \[\sqrt{50}A\]
d. \[0\]

Answer 1

Hint: The average value of all the instantaneous values of the current and voltage in an alternate form and when taken together form the average value. Thus the waves formed are that of sine and square sine waves. After taking the current wave in form of sine graph the value of the waveform is both positive and negative with the equation written as:
\[i={{i}_{o}}+\sin \omega t\]
where \[i\] is the current, \[{{i}_{o}}\] is the peak current form, \[\omega t\] is the phase angle.

Complete answer:
The average of the sine function for an entire time period of T is given as zero.
The following can be verified as the value of the sine graph when forming angles in form of \[n\pi \] i.e. \[n=2,4,6,....\]

Hence, the waveform equation with \[5\sin 100\pi t\] of which \[100\pi \] being the even value of \\pi \form the value of the part \[5\sin 100\pi t\] as zero. Thereby, the current form by the average value being zero due to \[5\sin 100\pi t\] as zero, the current form is:
\[i=\left( 5+5sin100\text{ }\pi t \right)A\] with \[\left( 5\sin 100\pi t \right)=0\]
\[i=5A\]
The average value of current with the average value over time being zero is \[i\text{ }=\text{ }5A\].

Hence, the correct answer is option (B).

Note: Aside from average value we have peak and RMS value as well, where peak value is the maximum value founded during one cycle period and RMS value is the time required for the current to pass the resistor until the resistor heats up to the same amount of that of the current passed.