A capacitor of unknown capacitance is connected across a battery of V volts. The charge stored in it is 360 C . When potential across the capacitor is reduced by 120 V, the charge stored in it becomes 120 C .
Calculate:
(i) The potential V and the unknown capacitance C.
(ii) What will be the charge stored in the capacitor, if the voltage applied had increased by 120V?
OR
A hollow cylindrical box of length 1m and area of cross-section 25cm2 is placed in a three dimensional coordinate system as shown in the figure. The electric field in the region is given by, where E is in NC-1 and x is in metres. Find:
(i) Net flux through the cylinder.
(ii) Charge enclosed by the cylinder.
The charge on an unknown capacitor is given by,
Q = CV
CV = 360 C ... (1)On reducing the potential by 120 V, charge on the capacitor is reduced which is given by,
Q’ = C(V-120)
C(V-120) = 120 C … (2)
On solving equation (1) and (2), we have
Unknown capacitance from equation (1),
Q = CV
ii) Charge on the capacitor, if voltage is increased by 120V
Q = C (V+120)
= 2 (180+120)
= 600 C
OR
i) Electric flux through a surface, 
Flux through the left surface, 
Since x = 1m,
ii) Using Gauss Theorem, we can calculate the charge inside the cylinder.
