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 Q=CV, and since the charge on both capacitors is equal you get


6C_a = 4 C_b


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


1(C_a+2 \mu F) = 9 C_b


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