In series LCR circuit the alternating emf 'e' and the current 'i' are given by the equations e = e_0 ω t , i = i_0 (ω t + (π)/(6)) . The average power dissipated in the circuit over a one complete cycle of A.C is ( 60 =

Question

Quantrex Academy · Accepted Answer

Correct answer: B. (e_0 i_0)/(4)

The given equations for alternating emf and current are:

e = e_0 \cos\omega t = e_0 \sin\left(\omega t + \dfrac{\pi}{2}\right)

i = i_0 \sin\left(\omega t + \dfrac{\pi}{6}\right)

The phase difference

\phi

between the emf and current is:

\phi = \dfrac{\pi}{2} - \dfrac{\pi}{6} = \dfrac{\pi}{3} = 60^{\circ}

The average power dissipated over one complete cycle is given by:

P_{avg} = e_{rms} i_{rms} \cos\phi

Substituting the values of

e_{rms}

,

i_{rms}

, and

\cos\phi

:

P_{avg} = \left(\dfrac{e_0}{\sqrt{2}}\right) \left(\dfrac{i_0}{\sqrt{2}}\right) \cos 60^{\circ}

P_{avg} = \dfrac{e_0 i_0}{2} \times \dfrac{1}{2} = \dfrac{e_0 i_0}{4}

Answer:

\dfrac{e_0 i_0}{4}

In series LCR circuit the alternating emf 'e' and the current 'i'...

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