1983E2. The series circuit shown above contains a resistance R=2×106 ohms, a capacitor of unknown capacitance C , and a battery of unknown emf E and negligible internal resistance. Initially the capacitor is uncharged and the switch S is open. At time t=0 the switch S is closed. For t>0 the current in the circuit is described by the equation:
i(t)=ioe−t/6 where io=10 microamperes and t is in seconds.
a. Determine the emf of the battery.
b. By evaluating an appropriate integral, develop an expression for the charge on the right-hand plate of the capacitor as a function of time for t>0.
c. On the axes below sketch a graph of the charge Q on the capacitor as a function of time t.
d. Determine the capacitance C.