Two capacitors a and b are connected in series across a 10v battery. The voltages across a and b are found to be 6V and 4V respectively. If another 2microfarad capacitor is connected across a the voltage across b increases to 9V. Calculate the capacitances of a and b.

Hw to do that sum?

You can use the relatonship , and since the charge on both capacitors is equal you get



Then when you add the 2 F capacitor to a it's capacitance becomes F, and since the votage across b is now 9 that means the voltage across a is 1. So your second equation is



Now you have two equations is two unknowns, and you can solve for the capacitances of a and b.