A current in circuit is given by i=3+4sinωt. Then the effective value of current is?

The effective value of current, also known as the root mean square (RMS) value, for a sinusoidal function is given by the formula:

I_RMS = √(I_avg² + (I_rms_sin_component)²)

Where:

• I_avg is the average or DC component of the current, and
• I_rms_sin_component is the RMS value of the sinusoidal component of the current.

In the given current function i = 3 + 4sinωt, the DC component I_avg is 3 A and the peak value of the sinusoidal component is 4 A.

The RMS value of the sinusoidal component is given by its peak value divided by the square root of 2. So, I_rms_sin_component = 4/√2 = 2.83 A (approx).

Substituting these values into the formula, we get:

I_RMS = √((3)² + (2.83)²) = √(9 + 7.9889) = √16.9889 = 4.12 A (approx).

So, the effective value of the current is approximately 4.12 A.