If a direct current of value a ampere is superimposed on an alternating current `1 = b sin omega t` flowing through a wire, what is the effective value of the resulting current in the circuit?

Explanation

As current at any instant in the circuit will be,
`i=i_(dc)+i+(ac)=a+bsinomegat`
So, `i_(eff)=[1/Tint_(0)^(T)(a+bsinomegat)^(2)dt]^(1//2)`
i.e., `=i_(eff)[1/Tint_(0)^(T)(a^(2)+2ab""sinomegat+b^(2)sin^(2)omegat)dt]^(1//2)`
but as
`1/Tint_(0)^(T)sinomegatdt=0 " and " 1/Tint_(0)^(T)sin^(2)omegatdt=1/2`
So, `i_(eff)=[a^(2)+1/2b^(2)]^(1//2)`