A 9.0V battery is connected in series with a 2.0kΩ resistor and a 4.7μF capacitor at time t=0. Neglect internal resistance of the battery.
(a) Calculate the time constant τ for this circuit.
(b) Determine the time required for the capacitor voltage to reach approximately 63% of its final value.
(c) At what time will the current in the circuit have dropped to one-tenth of its initial value? Justify your reasoning without deriving a full exponential expression.
(d) On qualitatively labeled axes (no numerical scale required), sketch both the current and the capacitor-voltage curves on the same set of axes from t=0 to a time of about 4τ. Indicate which curve corresponds to which quantity and show the location of the points you calculated in parts (b) and (c).