A variable condenser is permanently connected to a $100$ $V$ battery. If the capacity is changed from $2\,\mu \,F$ to $10\,\mu \,F$, then change in energy is equal to
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A capacitor $C_1$ is charged up to a voltage $V\, = 60\,V$ by connecting it to battery $B$ through switch $( 1)$, Now $C_1$ is disconnected from battery and connected to a circuit consisting of two uncharged capacitors $C_2\, = 3.0\,\mu F$ and $C_3\,= 6.0\,\mu F$ through a switch $(2)$ as shown in the figure. The sum of final charges on $C_2$ and $C_3$ is......$\mu C$
Two equal point charges are fixed at $x = - a$ and $x = + a$ on the $x-$axis. Another point charge $Q$ is placed at the origin. The Change in the electrical potential energy of $Q$, when it is displaced by a small distance $x$ along the $x$-axis, is approximately proportional to
A capacitor is connected to a $20\, {V}$ battery through a resistance of $10\, \Omega .$ It is found that the potential difference across the capacitor rises to $2\, {V}$ in $1\, \mu {s}$. The capacitance of the capacitor is $....\,\mu {F}$ Given : $\ln \left(\frac{10}{9}\right)=0.105$
For a charged spherical ball, electrostatic potential inside the ball varies with $r$ as $V =2 ar ^2+ b$. Here, $a$ and $b$ are constant and $r$ is the distance from the center. The volume charge density inside the ball is $-\lambda a \varepsilon$. The value of $\lambda$ is $...........$. $\varepsilon=$ permittivity of medium.
Two insulated metallic spheres of $3\,\mu F$ and $5\,\mu F$ capacitances are charged to $300\, V$ and $500\, V$ respectively. The energy loss, when they are connected by a wire is
A charge of $10\, e.s.u.$ is placed at a distance of $2\, cm$ from a charge of $40\, e.s.u.$ and $4\, cm$ from another charge of $20\, e.s.u.$ The potential energy of the charge $10\, e.s.u.$ is (in $ergs$)