workout 28b

workout 28b - HPHY 253 Workout 28b Series RC Circuits Dr....

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HPHY 253 Workout 28b Series RC Circuits Dr. A. E. Bak Name If a capacitor of capacitance C is being charged by a voltage source of electromotance E through a resistor of resistance R Q varies with time according to the relation Q ( t ) = Q max 1 e ± for a charging capacitor ; where Q max = C E is the maximum possible charge that the capacitor can acquire. The quantity ± RC is time constant . If a charged capacitor is discharging through a resistor, then we have Q ( t ) = Q 0 e for a discharging capacitor ; where Q 0 is the initial charge on the capacitor. On de±ning the capacitor current I C as I C ± ² ² ² ² dQ dt ² ² ² ² ; we ±nd that I C = Q max e = E R e for a charging capacitor and I C = Q 0 e for a discharging capacitor : Note that dQ=dt is the time rate at which the capacitor acquires charge. 1. 28 : 27 . Consider the series RC circuit of Active Figure 28 : 16 , for which R = 1 : 00 M , C = 5 : 00 ±F , and E = 30 : 0 V . (a) Find the time constant of the circuit. We have = RC = ³ 1 : 00 ² 10 6 ´ ³ 5 : 00 ² 10 6 ´ = 5 : 00 s as the time constant. (b) Find the maximum charge on the capacitor after the switch is thrown to position a , thereby connecting the capacitor to the battery. We have Q max = C E = ³ 5 : 00 ² 10 6 ´ (30 : 0) = 1 : 50 ² 10
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workout 28b - HPHY 253 Workout 28b Series RC Circuits Dr....

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