Question

A. Find the rms value of the resultant current in a wire which simultaneously has a direct current of 12.2A and sinusoidal alternating current of peak value of 12.2A
B. What would be the rms value of the current if the peak value of the sinusoidal alternating current is 10A and the DC current is increased to 20A

Answer 1

Part a

$I^2R = 12.2^2R+ (\frac{12.2}{\sqrt{12.2}})^2R\\ I^2=12.2^2+12.2\\ \mathrm{Add\:the\:numbers:}\:148.84+12.2=161.04\\ I^2=161.04\\ \mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\ I=\sqrt{161.04}\\ I=12.69015A$

Part b

$I^2R=10^2R+\left(\frac{20}{\sqrt{20}}\right)^2R\\ I^2=10^2+\left(\frac{20}{\sqrt{20}}\right)^2\\ I^2=10^2+2^2\cdot \:5\\ \mathrm{Add\:the\:numbers:}\:100+20=120\\ I^2=120\\ \mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\ I=\sqrt{120},\:I=-\sqrt{120}\\ I=2\sqrt{30}\\ I=10.95445A$