How Does Current Behave in a Discharging RC Circuit?

AI Thread Summary
The discussion focuses on calculating the current in a discharging RC circuit after 5 microseconds, with a capacitor of 400 pico farads charged to 10 volts through a 50kΩ resistor. The voltage across the capacitor after 5 microseconds is found to be approximately 7.788 volts using the equation Vc = Ve * e^(-t/CR). The current flowing at that time is calculated to be 0.156 mA by applying Ohm's law (i = Vr/R). The response confirms the calculations are correct and suggests an alternative method to express the current using the initial current and time constant. Overall, the calculations and methodology presented are validated.
brenfox
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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.
 
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brenfox said:

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 Io from the initial conditions.
 
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