An alternating current 'i' is given by 
. Then the avg current in the first one quarter time period is
Text Solution
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Define the Average Current Formula
The average current 
over a time interval 
can be expressed as:
Substitute the Expression for I
Substituting the expression for I into the average current formula:
Simplify the Sine Function
The sine function can be simplified:
Thus, we have:
Factor Out Constants
Since 
is a constant, we can factor it out of the integral:
Integrate the Cosine Function
To integrate 
:
Now, we evaluate the definite integral from 0 to 
:
Evaluate the Limits
Calculating the limits:
Substitute Back into the Average Current Formula
Now substitute this result back into the average current formula:
Thus, the average current over the first quarter of the time period is:
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