An AC current is given by I=I1 sinωt + I2 cosωt. A hot wire ammeter will give a reading :

a. \(\frac{I_{1}+I_{2}}{\sqrt{2}}\)

b. \(\sqrt{\frac{I_{1}^{2}+I_{2}^{2}}{2} }\)

c. \(\sqrt{\frac{I_{1}^{2}-I_{2}^{2}}{2} }\)

d. \(\frac{I_{1}+I_{2}}{2\sqrt{2}}\)

Answer: (b)

\(\begin{array}{l} \mathrm{I}_{\mathrm{RMS}}=\sqrt{\frac{\left[I^{2} d t\right.}{\mid d t}} \\ \mathrm{I}_{\mathrm{RMS}}^{2}=\int_{0}^{T} \frac{\left(I_{1} \sin \omega t+I_{2} \cos \omega t\right)^{2} d t} \ \end{array}\) \(= \frac{1}{T}\int_{0}^{T}(I^{2}_{1}sin^{2}\omega t+I^{2}_{2}cos^{2}\omega t+2I_{1}I_{2}sin\omega tcos\omega t)\) \(=\frac{I_{1}^{2}}{2}+\frac{I_{2}^{2}}{2}+0\) \(\mathrm{I}_{\mathrm{RMS}}=\sqrt{\frac{I_{1}^{2}+I_{2}^{2}}{2}}\)

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