a) If we wait an infinite amount of time what would the charge be on the capacit
ID: 1288034 • Letter: A
Question
a) If we wait an infinite amount of time what would the charge be on the capacitor?
b) How long does it take for the capacitor to charge up to 90% of the maximum possible charge?
c) If you wait until the capacitor is fully charged, how much energy is stored on the capacitor?
d) How much energy was dissipated in the resistor during the charging process?
Please give me a step by step solution. More detial and formula please!
I have a 10 volt battery making a circuit with a 1kohm resistor and a 100 Mu farad capacitor connected in series. At time t = 0, there is no charge on the capacitor but a switch closes allowing charge to flow out of the battery, through the resistor and onto the capacitor. a) If we wait an infinite amount of time what would the charge be on the capacitor? b) How long does it take for the capacitor to charge up to 90% of the maximum possible charge? c) If you wait until the capacitor is fully charged, how much energy is stored on the capacitor? d) How much energy was dissipated in the resistor during the charging process? Please give me a step by step solution. More detial and formula please!Explanation / Answer
an infinite time,
charge Q = Qo (1-e^-t/RC)
Q = Qmax = Q0 = CV 100e-6*10 = 1 mC
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apply 1-e^-t/RC = 0.9
e^-t/RC = 1-0.9 =0.1
-t/RC = ln (0.1)
-t/Rc = -2.302
t = 2.302* 1000 * 100e-6
t = 0.2303 secs
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energy U = 0.5 Q^2/C
U = 0.5* 1e-3*1.e-3/(100e-6)
U = 5 mJ
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energy across resistor E = V^2t/R
E = 5 mJ
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