# finding current in inductor. series RLC. piecewise voltage source.

#### John Christopher Martin

Joined Jan 10, 2016
3
here is the question.

(1 point) A 5 mH inductor, a 25 μF capacitor, and a 20 Ω resistor are in series with a voltage source vs(t). The voltage source is zero prior to t=0. At t=0, it jumps to 75 V. At t=1 ms, it drops to zero. At t=2 ms it again jumps to 75 V, and it continues in the same periodic fashion. Find the current the source supplies at:
(a) t=0−
(b) t=0+
(c) t=1 ms
(d) t=2 ms

I was able to figure out a, b, and c. I don't know what to do to get (d).

#### WBahn

Joined Mar 31, 2012
26,398
What is different about (d) relative to (c) that is causing problems?

#### RBR1317

Joined Nov 13, 2010
690
For part (d) would you calculate the response for t=2- or t=2+? Would it make a difference? Did it make a difference for part (a) & part (b)?

If you form the input pulse from the superposition of time-shifted step functions, can you then calculate the pulse response as the superposition of the responses to time-shifted step functions?

#### WBahn

Joined Mar 31, 2012
26,398
What analysis tools do you presently have available to you? Have you been introduces to Laplace transforms yet?

#### Bordodynov

Joined May 20, 2015
2,983

#### MrAl

Joined Jun 17, 2014
8,874
here is the question.

(1 point) A 5 mH inductor, a 25 μF capacitor, and a 20 Ω resistor are in series with a voltage source vs(t). The voltage source is zero prior to t=0. At t=0, it jumps to 75 V. At t=1 ms, it drops to zero. At t=2 ms it again jumps to 75 V, and it continues in the same periodic fashion. Find the current the source supplies at:
(a) t=0−
(b) t=0+
(c) t=1 ms
(d) t=2 ms

I was able to figure out a, b, and c. I don't know what to do to get (d).
Hi,

The main thing here is that for the second pulse there will be initial conditions to deal with. The first pulse establishes initial conditions that will be present when the second pulse arrives. What this usually means is you would write the equations for the RLC circuit but those equations would also contain expressions for the initial conditions, and one way to do this is to add initial condition generators to the circuit before you start. Once you have those equations, for the first pulse you set all initial conditions to zero, then at the end of the first period just before the start of the next pulse you use the solution results for the voltage across the cap and the current through the inductor as the initial conditions for the next pulse.
So really you have to solve for the desired response(s) AND the additional responses of the voltage across the cap and the current through the inductor. This gives you solutions for any pulse at any time later.
If you need to solve for a pulse train in closed form that is a bit more difficult so we'll wait on that one. For now it just seems you need to solve for two pulses and that is a lot easier.

Also as others have already suggested, it would be good if you could describe your math background a little so we know what kind of solution will be acceptable to you at this point in your studies. For example, Laplace, State Space, etc.