An alternating current is given by I = IA sin ωt + IB cos ωt. The r.m.s. current will be :

Question

An alternating current is given by

\(\mathrm{I}=\mathrm{I}_{\mathrm{A}} \sin \omega \mathrm{t}+\mathrm{I}_{\mathrm{B}} \cos \omega \mathrm{t}\)

The r.m.s. current will be :

(1) \(\sqrt{\mathrm{I}_{\mathrm{A}}^{2}+\mathrm{I}_{\mathrm{B}}^{2}}\)

(2) \(\frac{\sqrt{\mathrm{I}_{\mathrm{A}}^{2}+\mathrm{I}_{\mathrm{B}}^{2}}}{2}\)

(3) \(\sqrt{\frac{\mathrm{I}_{\mathrm{A}}^{2}+\mathrm{I}_{\mathrm{B}}^{2}}{2}}\)

(4) \(\frac{\left|I_{A}+I_{B}\right|}{\sqrt{2}}\)

Answer 1

Correct option is : (3) \(\sqrt{\frac{\mathrm{I}_{\mathrm{A}}^{2}+\mathrm{I}_{\mathrm{B}}^{2}}{2}}\) 

 \( i_{\text {rms }}=\sqrt{\frac{\int I^{2} d t}{\int d t}}\)

\( \sqrt{\frac{I_{A}^{2}+I_{B}^{2}}{2}}=i_{\text {rms }}\)