A parallel plate capacitor $\mathrm{C}$ with plates of unit area and separation $\mathrm{d}$ is filled with a liquid of dielectric constant $\mathrm{K}=2$. The level of liquid is $\frac{\mathrm{d}}{3}$ initially. Suppose the liquid level decreases at a constant speed $V,$ the time constant as a function of time $t$ is Figure: $Image$
A parallel plate capacitor $\mathrm{C}$ with plates of unit area and separation $\mathrm{d}$ is filled with a liquid of dielectric constant $\mathrm{K}=2$. The level of liquid is $\frac{\mathrm{d}}{3}$ initially. Suppose the liquid level decreases at a constant speed $V,$ the time constant as a function of time $t$ is Figure: $Image$
- [IIT 2008]
- A
$\frac{6 \varepsilon_0 \mathrm{R}}{5 \mathrm{~d}+3 \mathrm{Vt}}$
- B
$\frac{(15 \mathrm{~d}+9 \mathrm{Vt}) \varepsilon_0 \mathrm{R}}{2 \mathrm{~d}^2-3 \mathrm{dVt}-9 \mathrm{~V}^2 \mathrm{t}^2}$
- C
$\frac{6 \varepsilon_0 \mathrm{R}}{5 \mathrm{~d}-3 \mathrm{Vt}}$
- D
$\frac{(15 \mathrm{~d}-9 \mathrm{Vt}) \varepsilon_0 \mathrm{R}}{2 \mathrm{~d}^2+3 \mathrm{dVt}-9 \mathrm{~V}^2 \mathrm{t}^2}$
Similar Questions
In a parallel plate capacitor set up, the plate area of capacitor is $2 \,m ^{2}$ and the plates are separated by $1\, m$. If the space between the plates are filled with a dielectric material of thickness $0.5\, m$ and area $2\, m ^{2}$ (see $fig.$) the capacitance of the set-up will be $.........\, \varepsilon_{0}$
(Dielectric constant of the material $=3.2$ ) and (Round off to the Nearest Integer)
In a parallel plate capacitor set up, the plate area of capacitor is $2 \,m ^{2}$ and the plates are separated by $1\, m$. If the space between the plates are filled with a dielectric material of thickness $0.5\, m$ and area $2\, m ^{2}$ (see $fig.$) the capacitance of the set-up will be $.........\, \varepsilon_{0}$
(Dielectric constant of the material $=3.2$ ) and (Round off to the Nearest Integer)
- [JEE MAIN 2021]
A capacitor is kept connected to the battery and a dielectric slab is inserted between the plates. During this process
A capacitor is kept connected to the battery and a dielectric slab is inserted between the plates. During this process
Define dielectric constant.
Define dielectric constant.
Match the pairs
Capacitor
Capacitance
$(A)$ Cylindrical capacitor
$(i)$ ${4\pi { \in _0}R}$
$(B)$ Spherical capacitor
$(ii)$ $\frac{{KA{ \in _0}}}{d}$
$(C)$ Parallel plate capacitor having dielectric between its plates
$(iii)$ $\frac{{2\pi{ \in _0}\ell }}{{ln\left( {{r_2}/{r_1}} \right)}}$
$(D)$ Isolated spherical conductor
$(iv)$ $\frac{{4\pi { \in _0}{r_1}{r_2}}}{{{r_2} - {r_1}}}$
Match the pairs
| Capacitor | Capacitance |
| $(A)$ Cylindrical capacitor | $(i)$ ${4\pi { \in _0}R}$ |
| $(B)$ Spherical capacitor | $(ii)$ $\frac{{KA{ \in _0}}}{d}$ |
| $(C)$ Parallel plate capacitor having dielectric between its plates | $(iii)$ $\frac{{2\pi{ \in _0}\ell }}{{ln\left( {{r_2}/{r_1}} \right)}}$ |
| $(D)$ Isolated spherical conductor | $(iv)$ $\frac{{4\pi { \in _0}{r_1}{r_2}}}{{{r_2} - {r_1}}}$ |
The potential gradient at which the dielectric of a condenser just gets punctured is called
The potential gradient at which the dielectric of a condenser just gets punctured is called