A 10 micro 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, curren

(a) Just after the circuit has been closed, the potential difference across the resistor is 0 V, as the capacitor is fully charged and acts as an open circuit. Therefore, no current flows through the resistor, and the charge on the capacitor is equal to the charge it was initially charged with. (b) 1 second after the circuit has been closed, the potential difference across the resistor is still 0 V, as the capacitor hasn't had enough time to discharge significantly. The current through the resistor can be calculated using Ohm's Law: I = V/R = 12 V / 100 k? = 0.12 mA. The charge on the capacitor can be calculated using the formula Q = CV, where C is the capacitance and V is the potential difference across it: Q = 10 ?F * 12 V = 0.12 mC. (c) 5 minutes after the circuit has been closed, the capacitor has had enough time to discharge significantly. The potential difference across the resistor can be calculated using the formula V = V0 * e^(-t/RC), where V0 is the initial potential difference, R is the resistance, C is the capacitance, and t is the time elapsed: V = 12 V * e^(-5*60 s / (100 k? * 10 ?F)) ? 2.2 V. The current through the resistor can be calculated using Ohm's Law: I = V/R = 2.2 V / 100 k? = 0.022 mA. The charge on the capacitor can be calculated using the formula Q = CV: Q = 10 ?F * 2.2 V = 0.022 mC.