A capacitor with an initial potential difference of 121 V is discharged through a resistor when a switch betwe?
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A capacitor with an initial potential difference of 121 V is discharged through a resistor when a switch between them is closed at t = 0 s. At t = 10.0 s, the potential difference across the capacitor is 1.09 V. (a) What is the time constant of the circuit? (b) What is the potential difference (in V) across the capacitor at t = 17.5 s?
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Answer:
voltage on a cap, discharging v = v₀e^(–t/RC) R is resistance in ohms, C is capacitance in farads t is time in seconds 1.09 = 121e^(–10/RC) e^(–10/RC) = 0.0090083 –10/RC = -4.7096 RC = 2.12 seconds (a) v = v₀e^(–t/RC) = 121e^(–17.5/2.12) = 0.0319 volts .
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