A direct current of 6 ~A is superimposed on an alternating current I=10 t flowing through a wire. The effective value of the resulting current will be

Step-by-step solution

Given, I=6+10 t aligned I_ eft & = [ . ₀^T I^2 d t ]^ 1 / 2 ₀^T d t = [ 1 T ₀^T(6+10 t)^2 d t ]^ 1 / 2 . & = [ 1 T ₀^T (36+120 t+100 ^2 t ) d t ]^ 1 / 2 aligned But as, 1 T ₀^T t d t=0 and 1 T ₀^T ^2 t= 1 2 I_ eff = [36+ 1 2 100 ]^ 1 / 2 =9.27 Thus, I_ eff =9.27 ~A .