A 2.00-nF capacitor with an initial charge of 4.90 µC is discharged through a 2.21-kΩ resistor.(a) Calculate the current in the resistor 9.00 µs after the resistor is connected across the terminals of the capacitor. (Let the positive direction of the current be define such that dQdt > 0.) mA(b) What charge remains on the capacitor after 8.00 µs? µC(c) What is the (magnitude of the) maximum current in the resistor?
Question
A 2.00-nF capacitor with an initial charge of 4.90 µC is discharged through a 2.21-kΩ resistor.(a) Calculate the current in the resistor 9.00 µs after the resistor is connected across the terminals of the capacitor. (Let the positive direction of the current be define such that dQdt > 0.) mA(b) What charge remains on the capacitor after 8.00 µs? µC(c) What is the (magnitude of the) maximum current in the resistor?
Solution
(a) The current in the resistor can be calculated using the formula for the current in a discharging RC circuit:
I = Q0/(RC) * e^(-t/RC)
where: I is the current, Q0 is the initial charge on the capacitor, R is the resistance, C is the capacitance, and t is the time.
Substituting the given values:
I = (4.90 µC) / (2.21 kΩ * 2.00 nF) * e^(-9.00 µs / (2.21 kΩ * 2.00 nF))
After calculating, you will get the current in the resistor 9.00 µs after the resistor is connected across the terminals of the capacitor.
(b) The charge remaining on the capacitor can be calculated using the formula for the charge on a discharging capacitor:
Q = Q0 * e^(-t/RC)
Substituting the given values:
Q = 4.90 µC * e^(-8.00 µs / (2.21 kΩ * 2.00 nF))
After calculating, you will get the charge that remains on the capacitor after 8.00 µs.
(c) The maximum current in the resistor occurs immediately after the resistor is connected across the terminals of the capacitor, at t = 0. At this time, the current is equal to the initial charge on the capacitor divided by the product of the resistance and the capacitance:
I_max = Q0 / (R*C)
Substituting the given values:
I_max = 4.90 µC / (2.21 kΩ * 2.00 nF)
After calculating, you will get the maximum current in the resistor.
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