Question

Need help with hand calculations!

Find VL (an equation that includes the input current pulse's delay) in the following circuit using the Laplace transform. Sketch VL from 0 to 1 us ensuring you label the axis. (15 points) 1. R1 VL 3K PULSE(-1mA 1mA 100n) L1 100uH R2 1k .tran 1u

Answer 1

This is an RL circuit. To know the behavior of this circuit we must note the following two points

1. The inductor current increases in an exponential manner as soon as the current is applied to it as shown below

Here $I_{f}$ is the final value of the current.

In this case, the equation of current is given as

Iz(t) = 1/(1-e

Here $\tau$ is the time constant of circuit and

TReq

Here
3k * 1k 9 3 1. = 0.75k12
and
L = 100μΗ

So,

100 * 10-6 Ren=0.75 + 103 = 0.134 Sec

So,

Iz(t) = 1/(1-e

and $V_{L}=L\frac{dI}{dt}=L\frac{d}{dt}(I_{f}(1-e^{\frac{-t}{\tau}}))=-\frac{LI_{f}}{\tau}e^{\frac{-t}{\tau}}$

2. When the input current becomes zero, the current from inductor decreases exponentially as shown below

So,

+31 = (1) 71

ulo? VL=LC - 20, P

Overall input and output

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