Please answer this question and all parts. Show all work. Thanks. [10 pts] In an
ID: 1584242 • Letter: P
Question
Please answer this question and all parts. Show all work. Thanks.
[10 pts] In an RC circuit, how many time constants must elapse if an initially uncharged capacitor is to reach 40% of its final potential difference? 9. Or, / Consider the following RC circuit. At the switch S is closed with the capacitor uncharged. Take C'-30 F, c 50 p, and R-10 2. (a) [3 pts] Apply Kirchhoff's Loop Rule to the circuit and write an equation for the circuit. -e } e (b) [3 pts] What is the charge on the capacitor when the current in the circuit is 2.0 mA? (C) [4 pts] At what time does the charge on the capacitor becomes 300p07 2Explanation / Answer
Solution) Final potential be V
40% of V
We have V=Vo(1-e^(-t/Rc))
(40/100)Vo=Vo(1-e^(-t/Rc))
0.4=1-e^(-t/Rc)
e^(t/Rc)=(1/0.6)
t/Rc=0.221
t=0.221Rc
Given here C=30uF
E=50V
R=10kohms
(a) loop equation
E-(Q/C)-IR=0
IR=E-(Q/c)
(b) I=2mA
Substituting in above equation
(2×10^(-3))(10×10^(3))=50-(Q/(30×10^(-6))
Q/(30×10^(-6))=30
Q=900×10^(-6)
Q=900uC
(c) Q=300uC
Qo=900uC
Q=Qo(1-e^(-t/Rc))
300=900(1-e^(-t/(10×10^(3)×30×10^(-6)))
e^(10t/3)=3/2
10t/3=log(1.5)
t=0.052 seconds