Question

A 2.02 nF capacitor with an initial charge of 4.55 µC is discharged through a 1.22 kΩ resistor. (a) Calculate the current in the resistor 9.00 µs after the resistor is connected across the terminals of the capacitor. mA (b) What charge remains on the capacitor after 8.00 µs? µC (c) What is the maximum current in the resistor? A

Answer 1

a) 0.048A

b) 0.18µC

c) 1.85A

Step-by-step explanation:

The discharged current of the capacitor as a function of time is given by:

`i=(q_o)/(RC)*e^{-(t)/(\tau)}\\where:\\\tau=RC\\`

`\tau=1.22*10^3*2.02*10^(-9)\\\tau=2.46*10^(-6)s`

a)

`i=(4.55\µC)/(2.46\µs)*e^{-(9\µs)/(2.46\µs)}\\\\i=0.048A`

b)

`q=q_o*e^{-(t)/(\tau)}`

`q=4.55\µC*e^{-(8\µs)/(2.46\µs)}\\q=0.18\µC`

c) the maximum current occurs when t=0

`i=(4.55\µC)/(2.46\µs)*e^{-(0\µs)/(2.46\µs)}\\\\i=1.85A`