An electric current consists of a steady direct current (DC) component I₀ and a sinusoidal alternating current (AC) component I₁ ( t) . If the overall root mean square (RMS) value of this mixed current is measured to be 3 times the DC component I₀ , the ratio of the peak value of the alternating current to the direct current ( I₁ I₀ ) is

Step-by-step solution

The instantaneous current is given by i(t) = I₀ + I₁ ( t) . The mean square value of the current over a complete cycle is: i^2 = (I₀ + I₁ ( t))^2 i^2 = I₀^2 + I₁^2 ^2( t) + 2I₀ I₁ ( t) Since the average value of ( t) over a full cycle is zero and the average value of ^2( t) is 1 2 , we get: I_ rms ^2 = I₀^2 + I₁^2 2 It is given that I_ rms = 3 I₀ . Substituting this into the equation: ( 3 I₀)^2 = I₀^2 + I₁^2 2 3 I₀^2 = I₀^2 + I₁^2 2 2 I₀^2 = I₁^2 2 I₁^2 = 4 I₀^2 Taking the square root of both sides: I₁ I₀ = 2 Answe