Answer: a.) V= 12V I=0.12mA and Q= 120mC b.) V= 4.32V I=0.0432mA and Q=43.2mC c.

Question

Answer: a.) V= 12V I=0.12mA and Q= 120mC b.) V= 4.32V I=0.0432mA and Q=43.2mC c.) V=0V I=0mA and Q=0
Please show work 28.4 A 10F capacitor has been charged to a potential difference of 12 V. A 100 k resistor is connected in series with the capacitor. (a) What are the potential difference across the resistor, current through the resistor, and charge on the capacitor just after the circuit has been closed? (b) What are the potential difference across the resistor, current through the resistor, and charge on the capacitor 1 second after the circuit has been closed? hat are the potential difference across the resistor, current through the resistor, and charge on the capacitor 5 minutes after the circuit has been closed?

Explanation / Answer

q = CE*(1-e^-(t/RC))

V = E*(1-e^-(t/RC))

i = E/R*e^-(t/Rc)

(a)

at t = 0

potential difference = 0

current i = E?R = 12/10000 = 12*10^-5 A

charge q = 0

(b)

at t = 1 s

potential difference = 12*(1-e^-(1/(100000*10*10^-6))) = 7.58 V

current i = (12/100000)*e^-(1/(100000*10*10^-6)) = 4.4*10^-5 A

charge q = 10*10^-6*12*(1-e^-(1/(100000*10*10^-6))) = 7.58*10^-5 C

(c)

at t = 5 min = 300 s

potential difference = 12*(1-e^-(300/(100000*10*10^-6))) = 12 V

current i = (12/100000)*e^-(300/(100000*10*10^-6)) = 0 A

charge q = 10*10^-6*12*(1-e^-(300/(100000*10*10^-6))) = 12*10^-5 C

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