The ratio of energy stored in capacitors `C_(1)` and `C_(2)`

Two capacitors C_1 and C_2 of capacitances C/2 and C/4 are connected to a V volt battery, as shown in figure. The ratio of energy slored in capacitors C_1 and C_2 is

(a) Find potential difference between A and B and C . (b) Find potential difference across capacitor C . (i) Find ratio of energy stored in capacitors, C_(1) and (C_2) (ii) If battery of emf of 2E is short -circuited, find charge flown in battery of emf 4E .

Capacitor C_(3) in the circuit is variable capacitor (its capacitance can be varied). Graph is plotted between potential difference V_(1) (across capacitor C_(1) ) versus C_(3) . Electric potential V_(1) approaches on asymptote of 10 volts as C_(3) to infty The ratio of energy stored in capacitor C_(1) to that of total energy when C_(3) toinfty is

Find currents I_(1),I_(2) and I_(3) and the energy stored in the capacitors C_(1) and C_(2) in the circuit shown in figure.

(i) Use Gauss's law to find the electric field due to a uniformly charged infinite plane sheet. What is the direction of field for positive and negative charge densities? (ii) Find the ratio of the potential differences that must be applied across the parallel and eries combination of two capacitors C_(1) and C_(2) with their capacitances in the ratio 1 : 2 so that the energy stored in the two of two capacitors C_(1) and C_(2) with their capacitances in the ratio 1 : 2 so that the energy stored in the two cases becomes the same.

Two capacitors of equal capacitance (C_(1)=C_(2)) are as shown in the figure. Initially, while the swithc is open (as shown) one of the capacitors is uncharged and the other carries charge Q_(0) . The energy stored in the charged capacitor is U_(0). Sometime after the switch is closed, the capacitors C_(1)"and" C_(2) carry charged Q_(1)"and"Q_(2) respectively, the energy stored in the capacitors are U_(1)"and"U_(2) respectively. Which of the following expression is correct?