QJEEM21Ph3c3e: JEE Main 2021 Physics - Class 12 JEEM21Ph3c3e Solution: An AC current is given by I = I 1 sin t + I 2 cos t. A hot wire …

Question

Verified Solution • 2025–26 Session moderate

An AC current is given by I = I₁ sin

\omega

t + I₂ cos

\omega

t. A hot wire ammeter will give a reading :

Accepted Answer

{I_{RMS}} = \sqrt {{{\int {{I^2}dt} } \over {\int {dt} }}}

I_{RMS}^2 = \int\limits_0^T {{{{{({I_1}\sin \omega t + {I_2}\cos \omega t)}^2}dt} \over T}}

= {1 \over T}\int\limits_0^T {(I_1^2{{\sin }^2}\omega t + I_2^2{{\cos }^2}\omega t + 2{I_1}{I_2}\sin \omega t\cos \omega t)dt}

= {{I_1^2} \over 2} + {{I_2^2} \over 2} + 0

{I_{RMS}} = \sqrt {{{I_1^2 + I_2^2} \over 2}}

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