
Two capacitors, of capacitances
and
, are connected in parallel to a power supply of electromotive force (e.m.f.)
, as shown in the figure below.
Show that the combined capacitance
of the two capacitors is given by

Explain your reasoning. You may draw on the figure above if you wish.
Two capacitors of capacitances
and
, and a resistor of resistance
, are connected into the circuit in the figure below.
The battery has an e.m.f. of
. Show that the combined capacitance of the two capacitors is
.