V = 12V I = 0.12mA and Q = 120mC V = 4.32V I = 0.0432mA and Q = 43.2mC V = 0V I
ID: 1494803 • Letter: V
Question
V = 12V I = 0.12mA and Q = 120mC V = 4.32V I = 0.0432mA and Q = 43.2mC V = 0V I = 0mA and Q = 0 A 10 mu F capacitor has been charged to a potential difference of 12 V. A 100 k Ohm resistor is connected in series with the capacitor. What are the potential difference across the resistor, current through the resistor, and charge on the capacitor just after the circuit has been closed? 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? What 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
a) Just after circuit has been closed,
Potential across Resistor = V = 12.0 V
Current across resistor = I = V/R = 0.12 mA
Charge across capacitor = 120 mC
b) Time constant = T = RC = 100*10^3*10*10^-6 = 1 sec
After 1 sec,
Potential across Capacitor = Vo*[1 – exp(-t/RC)] = 7.585 V
Potential across Resistor = V = 12.0 - 7.585 = 4.42 V
Current across resistor = I = V/R = 0. 0.0442 mA
Charge across capacitor = 120*exp(-t/RC) = 44.15 mC
c) After 300 sec,
Potential across Resistor = V = 0 V
Current across resistor = I = V/R = 0 mA
Charge across capacitor = 0
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