AC analysis intro 1

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Solving circuits with differential equations is hard. If we limit ourselves to sinusoidal input signals, a whole new method of AC analysis emerges.
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Shouldn't L(d^2i/dt^2) + R(di/dt) + (1/C)i = dv_in/dt. Instead of being equal to v_in?

colehill
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Isn't it L di/dt, not L di^2 / dt^2 ?

Enigma
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if the output of voltage of RL circuit is taken to be the voltage across the inductor, the circuit is said to be what

sammezdoodles
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The derivatives are rate of change of Voltage and not just Voltage

dutta.alankar
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can you please upload videos about regular rlc circuits (not ac circuits) ?
thank you very much! :)

bartalor