Three identical capacitors, $P, Q$ and $S$, each of the capacitance $C$, are connected to a battery of voltage $V$, as shown in the figure. If the energy stored in the capacitor $P$ and total energy stored in the system are $U_P$ and $U_T$, respectively, then the ratio $\frac{U_P}{U_T}$ is:

Five capacitors of capacitances

$C_1=C_2=C_3=C_4=10 \mu \mathrm{~F}$ and $C_5=2.5 \mu \mathrm{~F}$ are connected as shown, along with a battery of 50 V .

The equivalent capacitance and the charges on each capacitor respectively are:

Consider two uncharged capacitors of equal capacitance 200 pF . One of them is charged by a 100 V supply and disconnected. Now this capacitor is connected to the uncharged capacitor. The amount of electrostatic energy lost in the process is:

The plates of a parallel plate capacitor are separated by $d$. Two slabs of different dielectric constant $K_1$ and $K_2$ with thickness $\frac{3}{8} d$ and $\frac{d}{2}$, respectively are inserted in the capacitor. Due to this, the capacitance becomes two times larger than when there is nothing between the plates. If $K_1=1.25 K_2$, the value of $K_1$ is: