Problem 7: (8% of Assignment Value)
The circuit shown contains a voltage source with emf $\varepsilon$ = 2.99 V, a resistor with resistance R = 165 k$\Omega$,
and a capacitor with capacitance C = 547 nF. When switch S is set to position a, the three circuit elements
are in series. When the switch is in position b, the battery is excluded from the circuit. The switch is initially
moved to position a where it remains for a sufficiently long time that the capacitor is fully charged.
Part (a)
Calculate the maximum charge, in coulombs, on the capacitor.
Q =
C
Part (b)
The switch is moved from position a, but it is not connected to position b, so the circuit not a complete circuit. What will happen to the voltage across the capacitor?
Part (c)
The switch is now moved to position b. What is the magnitude of the instantaneous current, in amperes, through resistor at the instant the switch makes contact with
terminal b?
Part (d)
With time measured from the instant that switch S is closed in position b, enter an expression for the voltage across the capacitor as a function of time.
Part (e)
With time measured from the instant that switch S is closed in position b, calculate the time, in seconds, when the charge on the capacitor is one-half of its maximum
value.
Part (f)
Calculate the current through the resistor, in amperes, at time t = 120.5 ms after the switch is closed in position b.
