An infinite nonconducting sheet of charge has a surface charge density of $10^{-7}\ C/m^2$. The separation between two equipotential surfaces near the sheet whose potential differ by $ 5\,V$ is
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Capacitance of a parallel plate capacitor becomes $4/3$ times its original value if a dielectric slab of thickness $t = d/2$ is inserted between the plates ($d$ is the separation between the plates). The dielectric constant of the slab is
Two capacitors connected in parallel having the capacities ${C_1}$ and ${C_2}$ are given $'q'$ charge, which is distributed among them. The ratio of the charge on ${C_1}$ and ${C_2}$ will be
A parallel plate capacitor is charged and the charging battery is then disconnected. If the plates of the capacitor are moved further apart by means of insulating handles, then
A conducting body $1$ has some initial charge $Q$, and its capacitance is $C$. There are two other conducting bodies, $2$ and $3$, having capacitances : $C_2 = 2C$ and $C_3 \rightarrow \infty$ . Bodies $2 $ and $3 $ are initially uncharged. "Body $2$ is touched with body $1$. Then, body $2$ is removed from body $1 $ and touched with body $3$, and then removed." This process is repeated $N$ times. Then, the charge on body $1$ at the end must be
A capacitor of $10\,\mu F$ charged up to $250\, volts$ is connected in parallel with another capacitor of $5\,\mu F$ charged up to $100\, volts$. The common potential is.....$V$
A capacitor of $2\,\, \mu F$ is charged as shown in the diagram. When the switch $S$ is turned to position $2,$ the percentage of its stored energy dissipated is ......$\%$
Two metallic charged spheres whose radii are $20\,cm$ and $10\,cm$ respectively, have each $150\,micro - coulomb$ positive charge. The common potential after they are connected by a conducting wire is