- #1

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1. Homework Statement

1. Homework Statement

Find the impulse response relative to the

**v**voltage.

_{c}(t)NOTE: delta(t) is the exact dirac's delta of infinite amplitude, not an approximated peak.

## Homework Equations

**δ(t) = d θ(t) / dt**

## The Attempt at a Solution

First of all I have a doubt of theoretical nature. If we know that capacitor's voltage is a continuous function (

**v**), and know that

_{c}(0^{-}) = v_{c}(0^{+}**v**for

_{c}= 0**t < 0**, how can voltage change? Shouldn't it remain 0 for the impulse duration, considering the circuit completely ideal?

Anyway, is it correct to consider the impulse source as a step one, and then derivate the function?

Specifically talking, I found the Thevenin equivalent between a and b, and it comes out:

**R**

V

_{th}= 1,6344 ΩV

_{th}= -0.3313 VThen I calculate the step response as:

**v**

_{cθ}(t) = -0.3323 θ(t) (1 - e^{-t/1.6344})From here is it correct to just derivate this function to get the impulse response?

**v**

_{cδ}(t) = -0.3323/1.6344 e^{-t/1.6344}Thank you very much.