A capacitor stores $60\ \mu C$ charge when connected across a battery. When the gap between the plates is filled with a dielectric , a charge of $120\ \mu C$ flows through the battery , if the initial capacitance of the capacitor was $2\ \mu F$, the amount of heat produced when the dielectric is inserted.......$\mu J$
Diffcult
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A capacitor is connected to a $10\,V$ battery. The charge on the plates is $10\,\mu C$ when medium between plates is air. The charge on the plates become $100\,\mu C$ when space between plates is filled with oil. The dielectric constant of oil is
A charge $+q$ is fixed at each of the points $x = x_0,\,x = 3x_0,\,x = 5x_0$, .... upto $\infty $ on $X-$ axis and charge $-q$ is fixed on each of the points $x = 2x_0,\,x = 4x_0,\,x = 6x_0$, .... upto $\infty $ . Here $x_0$ is a positive constant. Take the potential at a point due to a charge $Q$ at a distance $r$ from it to be $\frac{Q}{{4\pi {\varepsilon _0}r}}$. Then the potential at the origin due to above system of charges will be
The diameter of each plate of an air capacitor is $4\,cm$. To make the capacity of this plate capacitor equal to that of $20\,cm$ diameter sphere, the distance between the plates will be
After the switch shown in figure $A$ is closed, there is current $i$ through resistance $R$. Figure $B$ indicates current variation curves $a, b, c$ and $d$ for four sets of values of $R$ and capacitance $C$:
$(i)$ $R_0$ and $C_0$, $(ii)$ $2R_0$ and $C_0$,
$(iii)$ $R_0$ and $2C_0$, $(iv)$ $2R_0$ and $2C_0$.
Which set goes with which curve?
The electric potential at any point as a function of distance $(x)$ in meter is given by $V = 5x^2 + 10x -9 \,(volt)$ Value of electric field at $x = 1$ is......$Vm^{-1}$
An infinite number of charges each numerically equal to q and of the same sign are placed along the $x-$ axis at $x = 1,2,4,8.... \,metres$. Then the electric potential at $x = 0$ due to this set of charges is