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LECT12_185191 - 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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RC circuit: charging At time t=0, close Switch
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RC circuit: charging Q(t): I(t): t ε /R 0.368 ε /R τ = RC t=0 t Q Δ V C Δ V R Ι 0 0 ε ε / R 0 0 ε C ε ε (1–e –(t/ τ ) ) C ε (1–e –(t/ τ ) ) ( ε / R) (e –(t/ τ ) ) ε (e –(t/ τ ) )
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Time constant τ = RC RC is called the time constant: it's a measure of how fast the capacitor is charged up. It has units of time: RC = (V/I)(q/V) = q/I = q / (q/t) = t At t = RC, Q(t) and Δ V C (t) go to 1 – 1/e = 0.63 of the final values At t= RC, I(t) and Δ V R (t) go to 1/e of the initial values
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Time constant τ = RC Think about why increasing R and/or C would increase the time to charge up the capacitor: When charging up: τ will increase with C because the capacitor can store more charge. Increases with R because the flow of current is lower.
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Time constant τ = RC
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You want to make a so-called flasher circuit that charges a capacitor through a resistor up to a voltage at which a neon bulb discharges once every 5.0 sec. If you have a 10 microfarad capacitor what resistor do you need? Solution: Have the flash point be equal to 0.63 Δ V C,max (I.e., let t= τ ) τ = RC R = τ /C = 5s/10 -6 F = 5 × 10 5 Ohms This is a very big resistance, but 5 seconds is pretty long in "circuit" time
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Discharging an RC circuit: First, disconnect from EMF source.
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