How Does Current Behave in a Discharging RC Circuit?

[brenfox]

Homework Statement

Determine the current flowing when the capacitor has been discharging for 5μs
Capacitance=400 pico farads which is charged to 10v through a 50kΩ resistor.

Homework Equations

Vc = ve-t/CR

The Attempt at a Solution

So Vc =Ve -t/CR
-t/CR = -5*10^-6/400*10^-12*50*10^3
Which equals -0.25 so...
Vc= 10*e-0.25
Vc = 10*0.7788
Vc = 7.788 volts after 5 micro seconds

To find the current flowing after 5 micro seconds
i = Vr/R since Vr=Vc Vc/R = 7.788/50000 = 0.156mA.
Am i in the right ball park with this? Any guidance will be greatly appreciated.

 

[gneill]

Homework Statement

Determine the current flowing when the capacitor has been discharging for 5μs
Capacitance=400 pico farads which is charged to 10v through a 50kΩ resistor.

Homework Equations

Vc = ve-t/CR

The Attempt at a Solution

So Vc =Ve -t/CR
-t/CR = -5*10^-6/400*10^-12*50*10^3
Which equals -0.25 so...
Vc= 10*e-0.25
Vc = 10*0.7788
Vc = 7.788 volts after 5 micro seconds

To find the current flowing after 5 micro seconds
i = Vr/R since Vr=Vc Vc/R = 7.788/50000 = 0.156mA.
Am i in the right ball park with this? Any guidance will be greatly appreciated.

Yup, looks fine.

You could also have written the expression for the current $I(t) = I_o e^{-\frac{t}{\tau}}$ using the initial current I_o from the initial conditions.