xercise 26.42 You connect a battery, resistor, and capacitor as in (Figure 1) cl
ID: 1430670 • Letter: X
Question
xercise 26.42 You connect a battery, resistor, and capacitor as in (Figure 1) closed at t = 0 when the current in the circut has magnitude 3.00 A, the charge on the capacitor is 40.0 x 10 C What is the emf of the battery? Express your answer with the appropriate units. 1 where R= 190 and C·9 00 x 10 6 F The switch s is e-alue Umits Part B At what time t after the switch is closed is the charge on the capacitor equal to 400× 10 6C, Express your answer with the appropriate units of 1 of 1 Switch E open Units Part c When the cument has magnitude 300 A at what rate is energy being stored in the capacitor?Explanation / Answer
a) current in circuit is 3A.
I(t) = (e/R) [ e^(-t/Rc)]
e^(-t/RC) = RI/e = 19 x 3 / e = 57/e
at the same time charge is 40 x 10^-6 C.
Q = e C [ 1 - e^(-t/RC) ]
putting values,
40 x 10^-6 = e (9 x 10^-6) [ 1 - 57/e ]
40 = 9e[ e - 57] / e
e - 57 =40/9
e = 61.44 volt
b) 40 x 10^-6 = 61.44 x 9 x 10^-6 [ 1 - e^(-t / RC) ]
0.0723 = 1 - e^-t/RC
-t /RC = ln(1- 0.0723)
t = 0.075 x 19 x 9 x 10^-6 = 1.28 x 10^-5 s
c) Power by battery = VI = 61.44 x 3 = 184.32 W
power dissipated through resistor = I^2 R = 3^2 19 = 171 W
by capacitor = 184.32 - 171 = 13.32 W
d) POwer by battery = VI = 61.44 x 3 = 184.32 W
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