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Three capacitors are connected to $D.C.$ source of $100\;volts$ shown in the adjoining figure. If the charge accumulated on plates of ${C_1},\;{C_2}$ and ${C_3}$ are ${q_a},\;{q_b},\;{q_c},{q_d}.{q_e}$ and ${q_f}$ respectively, then
Two capacitors having capacitance $C _{1}$ and $C _{2}$ respectively are connected as shown in figure. Initially, capacitor $C _{1}$ is charged to a potential difference $V$ volt by a battery. The battery is then removed and the charged capacitor $C_{1}$ is now connected to uncharged capacitor $C _{2}$ by closing the switch $S$. The amount of charge on the capacitor $C _{2}$, after equilibrium is
A charge $ + q$ is fixed at each of the points $x = {x_0},\,x = 3{x_0},\,x = 5{x_0}$..... $\infty$, on the $x - $axis and a charge $ - q$ is fixed at each of the points $x = 2{x_0},\,x = 4{x_0},x = 6{x_0}$,..... $\infty$. Here ${x_0}$ is a positive constant. Take the electric potential at a point due to a charge $Q$ at a distance $r$ from it to be $Q/(4\pi {\varepsilon _0}r)$. Then, the potential at the origin due to the above system of charges is
The electrostatic potential $V$ at a point on the circumference of a thin non-conducting disk of radius $r$ and uniform charge density $\sigma$ is given by equation $V = 4 \sigma r$. Which of the following expression correctly represents electrostatic energy stored in the electric field of a similar charged disk of radius $R$?
Seven capacitors, each of the capacitance $2\,\mu F$, are to be connected in a configuration to obtain an effective capacitance of $\left( {\frac{6}{{13}}} \right)\,\mu F$. Which of the combinations, shown in figures below, will achieve the desired value ?