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Home » For an LCR circuit driven at frequency ω, the equation reads L di/dt + Ri + q/C = vi = vm sin ꞷ t(i) Multiply the equation by i and simplify where possible.(ii) Interpret each term physically.
For an LCR circuit driven at frequency ω, the equation reads L di/dt + Ri + q/C = vi = vm sin ꞷ t
(i) Multiply the equation by i and simplify where possible.
(ii) Interpret each term physically.
Alternating Current | CBSE | Class 12 | NCERT Exemplar | Physics
For an LCR circuit driven at frequency ω, the equation reads L di/dt + Ri + q/C = vi = vm sin ꞷ t
(i) Multiply the equation by i and simplify where possible.
(ii) Interpret each term physically.

Given equation is,

L d i / d t+R i+q / C=v i=v m \sin \omega t

i) On multiplying the above equation with I, we get,
\mathrm{d}\left(1 / 2 \mathrm{Li}^{2}\right) / \mathrm{dt}+1 / 2 \mathrm{C} \mathrm{dq}^{2} / \mathrm{dt}+\mathrm{i}^{2} \mathrm{R} / 2=1 / 2 \mathrm{Vm} \mathrm{i} \sin \omega \mathrm{t}

ii) \mathrm{d}\left(1 / 2 \mathrm{Li}^{2}\right) / \mathrm{dt} is representing the rate of change of potential energy in inductance \mathrm{L}

\mathrm{d} / \mathrm{dt} (\mathrm{q}^{2} / 2 \mathrm{C}) is representing the energy stored in dt time in the capacitor

\mathrm{i}^{2} \mathrm{R} is representing the joules heating loss

1 / 2 \operatorname{Vm} i \sin \omega t is the rate of driving force

i

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