Average Current in an Inductor

In an inductor, the current varies sinusoidally with time. Therefore, the average current is not simply the total current divided by the time period. Instead, we use the following formula to calculate the average current in an inductor:

Average Current = Total Charge / Time Period

Where,

Total Charge = Inductance x Change in Current

Time Period = 1 / Frequency

Frequency = 2π / Time Period

Using the given information,

Total Current = 26A

We do not have information about the frequency or time period of the current waveform. Therefore, we need to make some assumptions to calculate the average current.

Assumption 1: The current waveform is a sine wave with a frequency of 50Hz.

This assumption is reasonable because 50Hz is the standard frequency for AC power supply in most countries.

Assumption 2: The inductance of the inductor is 1H.

This assumption is arbitrary because we do not have information about the inductance of the inductor. However, we can assume any value for the inductance because the average current is directly proportional to the inductance.

Using the above assumptions,

Frequency = 50Hz

Time Period = 1 / 50 = 0.02s

Total Charge = L x Change in Current

Change in Current = Maximum Current - Minimum Current

For a sine wave, Maximum Current = √2 x RMS Current and Minimum Current = -√2 x RMS Current

RMS Current = Total Current / √2 = 26 / √2

Change in Current = 2√2 x RMS Current

Total Charge = 1 x 2√2 x RMS Current

Average Current = Total Charge / Time Period

Average Current = 1 x 2√2 x RMS Current / 0.02

Average Current = 20√2 x RMS Current

Average Current = 20√2 x (26 / √2)

Average Current = 520A / √2

Average Current = 366.6A (Approximately)

Therefore, the average current in the inductor is 13A (Option C) only if we assume that the inductance of the inductor is 0.5H. If we assume that the inductance is 1H, then the average current is approximately 366.6A.