RLC circuits help

Question

An RLC circuit has a resistor of 24kΩ, a capacitor of 15μF, and an inductor of 10mH. If the capacitor is charge to 10V at time t = 2, what is the voltage on the capacitor after 3 seconds?

Answer 1

This problem is strongly analogous to the damped harmonic oscillator. The correspondences are

m → 1/C

b → R

m → L

Since R² >> L/C for this case, the circuit is strongly over damped. That is to say, the inductor plays only a tiny role.

There will be one very short time constant and one which is (to a very good approximation) the usual RC time constant . For this case RC = .36 s.

Assuming that, in the charging the capacitor to 10 V in 2 seconds, no high frequency source was used, and the capacitor charged up slowly with the .36 s time constant. , the relevant equations are those of the RC type circuit.

V(3) / V(2) = V(3)/10 = ( 1- exp(-3/.36) ) /( 1 -exp(-2/.36) )

which works out to v(3) = 10.0364 V