Capacitors in Series and Parallel
Parallel adds area to grow the capacitance
Attach a second capacitor C2 in parallel with C1 = 4 μF and slide C2. The two plate areas join, so the parallel capacitance C_p = C1 + C2 grows straight away. The series combination C_s of the same two is always smaller than either. Set C2 so the parallel capacitance reaches the target of 10 μF.
In parallel the plate areas add
A capacitor’s capacitance is proportional to its plate area. In C = εA/d, double the area A and you double the capacitance. Wire two capacitors in parallel and the same voltage sits across both plate pairs, as if you had widened the plates and added their areas. So parallel capacitances simply add: C_p = C1 + C2. More area holds more charge, so the combination is larger than either one alone.
In series the reciprocals add
In series the same charge passes through both capacitors. The charge Q is common while the voltage splits, V = V1 + V2, and since V = Q/C this gives Q/C_s = Q/C1 + Q/C2, that is 1/C_s = 1/C1 + 1/C2. Tidied up, C_s = C1·C2/(C1+C2), so the series capacitance is always smaller than the smaller of the two. Picture the plate gap d growing and the drop in capacitance feels natural.
It is exactly opposite to resistors
Resistors add in series and add reciprocals in parallel. Capacitors swap those two: they add in parallel and add reciprocals in series. The same mirror holds against inductors — inductors add in series like resistors, and capacitors do the reverse. When in doubt, picture the area: parallel widens the plates and adds area, which is why the capacitance grows.
Back to the first screen
The larger C2, the longer the parallel bar grew straight away, reaching 10 μF when C2 was 6 μF (C1 = 4). The series bar of the same two stayed shorter than the smaller of them throughout. Parallel grows because widening the plates adds area; series shrinks because the charge is shared, the voltage splits, and reciprocals add. Flip the resistor rules and you have capacitors.