Question

Q/For the circuit showm bellow:

a) find the mathematical expression for the transient behavior of ve and ic after closing the switeh,
b) sketch vc and ic.
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Answer 1

hello your question is incomplete attached is the complete question

A) Vc = 15 ( 1 -
`e^(-t/0.15s)` ) , ic =
`1.5 mAe^(-t/0.15s)`

B) attached is the relevant sketch

Step-by-step explanation:

applying Thevenin's theorem to find the mathematical expression for the transient behavior of Vc and ic after closing the switch

`R_(th)` = 8 k ohms || 24 k ohms = 6 k ohms

`E_(th)` =
`(20 k ohms(20 v))/(24 k ohms + 8 k ohms)` = 15 v

t = RC = (10 k ohms( 15 uF) = 0.15 s

Also; Vc =
`E( 1 - e^(-t/t) )`

hence Vc = 15 ( 1 -
`e^(-t/0.15)` )

ic =
`(E)/(R) e^(-t/t)` =
`(15)/(10) e^(-t/t)` =
`1.5 mAe^(-t/0.15s)`

attached