CapacitorsCapacitors

Be aware that in applying the capacitance formula, C = Q/V (where C is the capacitance, Q is the charge and V is the voltage), the magnitude of charges on each plates must be equal and the charges are of opposite polarity. This is the condition that needs to be satisfied before using the said formula.

Now, the question gives that the charges on each of the capacitor plates are NOT equal (900 uC and 100 uC), thus the formula C = Q/V CANNOT be directly applied.

The capacitance of a capacitor is fixed, independent of the amount of charges on its plates. You could, therefore, imagine that you give the SAME AMOUNT of -ve charges to each plates in a view to achieving finally "equal magnitude of charges with opposite polarity (sign)" on the plates. This would not alter the voltage across the plates, but enables the application of the formula: C = Q/V

Clearly, it is not difficult to figure out if -500 uC (found by (900+100)/2 uC = 500 uC) is given to each plate, the one initially with 900 uC becomes (900 + (-500)) uC = +400 uC, and the one initially with 100 uC now becomes (100 + (-500)) uC = -400 uC. Now, the plates have equal amount of charges but with opposite signs, the formaul C = Q/V can apply.

Because equal amounts (-500 uC) of charges have been given to each plates, this doesn't change the voltage between the plates. The voltage thus remains at 4 v.

Capacitance = 400/4 uF = 100 uF