Using Laplace to solve circuit analysis

Cocoleia · Apr 19, 2017

Homework Statement

Circuit schematic with a 12 V voltage source, a switch marked t = 0, a 2 Ω resistor, a 5 H inductor carrying current i(t), and another 2 Ω resistor, next to the problem statement and answer i(t) = −3(1 + e^−0.8t) A for t > 0.

The Attempt at a Solution

Handwritten circuit analysis on lined paper: a t<0 circuit with a 12 V source and 2 ohm resistor giving I(0) = 12/2 = 6 A, and a t>0 circuit with a 2 ohm resistor, 5 H inductor and 30 V source, with mesh equation 12 + 4I(s) + 5s I(s) = 30, I(s)(4+5s) = 18, I(s) = 18/(4+5s), and inverse Laplace result i(t) = 3.6 e^(-0.8t).

As you can see, the answer is given in the problem. I have the 0.8t par right but somewhere along the way I messed up. I'm not really to sure about how to solve these types of problems using Laplace. Is there a general procedure that I should be following that I am not?

gneill · Apr 19, 2017

The Laplace transform of a DC source is V/s. Essentially it's modeled as a step function, "turning on" at time t = 0. So your 12 V source should be 12/s.

The voltage that represents the stored energy due to the initial current (your 30 V supply) needs to have its polarity reflect the actual direction of that initial current.

Otherwise you seem to be doing okay.

Using Laplace to solve circuit analysis

Homework Statement

The Attempt at a Solution

Discussion

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