The current output from of an a.c. source is given as I = 10 sin to t. The d.c equivalent of the current is
Question 1 Report
The current output from of an a.c. source is given as I = 10 sin to t. The d.c equivalent of the current is
Answer Details
The given equation of current, I = 10 sin ωt represents an alternating current (a.c.) which varies sinusoidally with time. The maximum value of this current is 10A, which occurs when sin ωt = 1. However, the question asks for the DC equivalent of this current, which is the constant value of current that would produce the same amount of heat in a resistor as the given a.c. current.
The DC equivalent of an AC current is the root mean square (rms) value of the AC current, which is the square root of the mean of the square of the current over one cycle. For a sinusoidal current, the rms value is given by the formula I_rms = I_max/√2.
Substituting the given maximum value of current (10A) into the formula for rms current gives:
I_rms = 10A/√2 = 7.07A (approx)
Therefore, the DC equivalent of the given AC current is approximately 7.1A, which is option (B) in the answer choices.
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