How Does a Capacitor Behave in a Simple Circuit?

[Timiop2008]

A working circuit contains a 3V power supply, a 5000uF Capacitor, and a 200ohm resistor.

a) What is the time constant for the circuit?
b) What is the charge in coloumbs on the capacitor at a potential difference of 3V?
c) How much energy is stored on the Capacitor at a potential difference of 3V?
d) Calculate the initial value of the current when the fully charged capacitor starts to discharge through the resistor.

Attempt:
a) T=RC
= 200 X (5000X10^-3)
=1000 seconds

b) Q=CV
Q = 5000X10^-3 X3
= 15C

c) E=1/2CV²
E=1/2 X 5000X10^-3 X 3²
E = 22.5J

d) Q=Q₀e^-t/RC

 

[fluidistic]

A working circuit contains a 3V power supply, a 5000uF Capacitor, and a 200ohm resistor.

a) What is the time constant for the circuit?
b) What is the charge in coloumbs on the capacitor at a potential difference of 3V?
c) How much energy is stored on the Capacitor at a potential difference of 3V?
d) Calculate the initial value of the current when the fully charged capacitor starts to discharge through the resistor.

Attempt:
a) T=RC
= 200 X (5000X10^-3)
=1000 seconds

b) Q=CV
Q = 5000X10^-3 X3
= 15C

c) E=1/2CV²
E=1/2 X 5000X10^-3 X 3²
E = 22.5J

d) Q=Q₀e^-t/RC

I think you did everything fine until the d) part. Currents are measured in amperes. What you wrote is the charge of the capacitor. How is i(t) related to q(t)? What you wrote is q(t).
How much is worth t when the capacitor starts to discharge?

 

[kerimek]

I=dQ/dt=-Q0/RCe-t/RC
At t=0, Q=CV=15C
Therefore, I=15/(200X5000X10-3)e0
I = 0.03A or 30mA

Overall, the time constant of the circuit is 1000 seconds, the charge on the capacitor at 3V is 15C, the energy stored on the capacitor at 3V is 22.5J, and the initial current when the capacitor starts to discharge is 0.03A or 30mA. This information can be useful in understanding the behavior and characteristics of the circuit, and can aid in making adjustments or improvements for optimal performance.