# Electric Transients

I would really appreciate if anyone could help me figure out these problems...

An RC circuit has a time constant of 40 microseconds. If the capacitor is first charged to a voltage of 80 volts and the RC circuit is then closed upon itself, after what time will the capacitor voltage be equal to 5 volts?... and

An RC circuit has a time constant of 0.0001 second. If the capacitor C is charged to 100 volts and, with the battery removed, the capacitor is then allowed to discharge through the resistor, at what time after being connected to the resistor will the voltage be 20 volts? (Assume that, in discharging, the voltage V at any time is equal to V=V(0) e^(-1/RC), where V(0) is the voltage to which C was charged.)

Thank you so much guys...

Astronuc
Staff Emeritus
Can you write out the formula for voltage or charge as a function of time, given the time constant?

Then we can point you in the right direction if necessary.

SGT
cunhasb said:
I would really appreciate if anyone could help me figure out these problems...

An RC circuit has a time constant of 40 microseconds. If the capacitor is first charged to a voltage of 80 volts and the RC circuit is then closed upon itself, after what time will the capacitor voltage be equal to 5 volts?... and

An RC circuit has a time constant of 0.0001 second. If the capacitor C is charged to 100 volts and, with the battery removed, the capacitor is then allowed to discharge through the resistor, at what time after being connected to the resistor will the voltage be 20 volts? (Assume that, in discharging, the voltage V at any time is equal to V=V(0) e^(-1/RC), where V(0) is the voltage to which C was charged.)

Thank you so much guys...
Your formula is independent ot the time. The correct formula would be:
$$V(t) = V(0)e^{-\frac{t}{RC}}$$
Where $$RC$$ is the time constant. If you replace V(0) with the initial value of the voltage and V(t) with the final value, you can use logarithms to solve for the time $$t$$.

Thank you so much guys...

well... I think I got it... correct me if I'm wrong...

1) Rc= 40 micro V(0) = 80 T=? V = 5V

V=v(0) e^(-t/RC)
5=80*e^(-t/RC)
5/80=e^(-t/RC)
RC*ln0.0625=-t
t=110.903 microseconds...

2) Rc= 0.0001 V(0) = 100 T=? V = 20V

V=v(0) e^(-t/RC)
20=100*e^(-t/RC)
20/100=e^(-t/RC)
RC*ln0.2=-t
t=160.94 microseconds...

SGT
That's it.