LECT11_185 - 18.5 RC Circuits Introduction to...

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18.5 RC Circuits Introduction to time-dependent currents and voltages. Applications: timing circuits, clocks, computers, charging + discharging capacitors
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An RC circuit
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RC circuit: charging At time t=0, close Switch
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An RC circuit At time t=0, close switch Initially (at t=0), Q = 0. Δ V C (at t=0) = Q(t=0) / C = 0 Loop Rule: ΣΔ V=0 = + ε - Δ V R - Δ V C + ε - IR - Δ V C = 0 So when charge = 0 (which occurs at t=0), ε = IR and so I = ε /R (at this instant, capacitor has no effect)
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RC circuit: charging Immediately after time t=0: Current starts to flow. Charge starts to accumulate on Capacitor (at a rate I=dQ/dt). As Q increases over time, Δ V C =Q/C also increases. But remember Δ V C + Δ V R = ε . So Δ V R is decreasing over time. And I through the resistor = Δ V R /R is also decreasing.
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RC circuit: charging After a very long time: Charge accumulates until Q reaches its maximum: Δ V C goes to ε . Total Q on the capacitor goes to C ε . + ε = Δ V C + Δ V R Δ V R goes to zero. And I goes to zero.
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RC circuit: charging Q(t): I(t): t ε /R 0.368 ε /R τ = RC t=0 t
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