the laplace transform of a capacitor's equation

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For a capacitor that is represented by a time-domain equation: v(t) =
1/C ∫i(τ)dτ + v(0), how do i do the laplace transform of v(t)

ive read the solution on a text book but just can't figure out how to
get to it.



Many thanks

 

[Noway2]

For a capacitor that is represented by a time-domain equation: v(t) =
1/C ∫i(τ)dτ + v(0), how do i do the laplace transform of v(t)

ive read the solution on a text book but just can't figure out how to
get to it.



Many thanks

There are two ways to apply the laplace transform. The hard way is to
apply it by cranking through the definition.

The easy way is to look it up in a table. In the case of your
question, the voltage of the capacitor is related to the integral of
the current, with an initial condition where the 1/C is a constant.
Once you look at the problem this way, it should be fairly straight
forward to find the answer.

Note, if this is for school work, you will still need to know how to
apply the definition to get the answer as you will most assuredly be
tested on this.