C

Step 1: Define the components of the current.
The total current consists of a 5 A D.C. component and a 60 Hz A.C. sinusoidal component with a peak value of 4 A.
Step 2: Write the expression for the A.C. component.
The sinusoidal A.C. component can be expressed as:
$$ I_{AC}(t) = I_{peak} imes ext{sin}(2 heta) = 4 imes ext{sin}(2 heta) $$
Step 3: Combine A.C. and D.C. components.
The total current is:
$$ I(t) = I_{DC} + I_{AC}(t) $$
Thus,
$$ I(t) = 5 + 4 imes ext{sin}(2 heta) $$
Step 4: Calculate average current over one cycle.
The average value of A.C. over one complete cycle is zero, therefore the average current is simply the D.C. component:
$$ I_{avg} = 5 ext{ A} $$
Step 5: Calculate effective (RMS) value of the current.
The RMS value of the A.C. component can be calculated as
$$ I_{rms(AC)} = \frac{I_{peak}}{\sqrt{2}} = \frac{4}{\sqrt{2}} = 2 \sqrt{2} ext{ A} $$
The effective value of the total current is given by:
$$ I_{rms(total)} = \sqrt{I_{DC}^2 + I_{rms(AC)}^2} $$
Thus,
$$ I_{rms(total)} = \sqrt{5^2 + (2 \sqrt{2})^2} = \sqrt{25 + 8} = \sqrt{33} ext{ A} $$
Final Results:
Average current is 5 A and effective current is \sqrt{33} A.
Therefore, the effective value of the total current is approximately 5.74 A.