Tag: capacitance of isolated bodies

Questions Related to capacitance of isolated bodies

The inductance of the oscillatory circuit of a radio station is 10 milli henry band its capacitance is $0.25 \mu F$. Taking the effect of the resistance negligible, wavelength of the broadcasted waves will be (velocity of light = $3.0  \ 10 ^4 \ m/s, \pi = 3.14$):

capacitance of an isolated spherical conductor capacitance of isolated bodies capacitance physics

  1. $9,42 \times 10^4 m$

  2. $18.8 \times 10^4 m$

  3. $4.5 \times 10^4 m$

  4. $none\ of\ these$

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Correct Option: C

The capacitance of an air filled parallel plate capacitor is $10\times {10}^{-12}F$. The separation between the plates is doubled and the space between the plates is then filled with wax giving the capacitance a new value of $40\times {10}^{-12}F$. The dielectric constant of wax is:

capacitance of an isolated spherical conductor capacitance of isolated bodies capacitance physics

  1. $12.0$

  2. $10.0$

  3. $8.0$

  4. $4.2$

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Correct Option: C
Explanation:

${C} _{1}=\cfrac{{ \varepsilon  } _{ 0 }A}{d}$ and ${C} _{2}=\cfrac{K{ \varepsilon  } _{ 0 }A}{2d}$
$\Rightarrow$ $\cfrac{{C} _{2}}{{C} _{1}}=\cfrac{K}{2}=\cfrac{40\times {10}^{-12}}{10\times {10}^{-12}}$
$\Rightarrow$ $K=8$

Each plate of parallel plate capacitor has a charge q on it. The capacitor is now connected to a battery. Now,

capacitance of an isolated spherical conductor capacitance of isolated bodies capacitance physics

  1. the facing surfaces of the capacitor have equal and opposite charges

  2. the two plates of the capacitor have equal and opposite charges

  3. the battery supplies equal and opposite charges to the two plates

  4. the outer surfaces of the plates have equal charges

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Correct Option: A,C,D

We assume that earth is at zero potential because capacitance of the earth is

capacitance of an isolated spherical conductor capacitance of isolated bodies capacitance physics

  1. infinite

  2. zero

  3. cannot say

  4. $10^6 farad$

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Correct Option: A
Explanation:

Because earth can store infinite charge so its capacitance is infinite, therefore it is at a zero potential. 

$\left (C=\dfrac {q}{V}\right )$.

1000 drops ofwater each of radius r and charged to a potential V coalesce together to form a big drop. The potential of big drop will be

capacitance of an isolated spherical conductor capacitance of isolated bodies capacitance physics

  1. 10 V

  2. 100 V

  3. 1000V

  4. $\displaystyle \frac{V}{100}$

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Correct Option: B
Explanation:

Vol. of the big drop =1000 *vol. of each small drop
$\displaystyle \frac{4}{3} \pi R^3 = 1000\times \frac{4}{3} \pi r^3$
$\Rightarrow R^3 = (10r)^3$
$\Rightarrow $ R =10r
Potential of each charged sphere for small drop, V = $\displaystyle \frac{q}{c}$
$\therefore$ Potential for the big drop = $1000 \displaystyle \frac{q}{C}$
We have, $C= 4 \pi \epsilon _0 R = 4 \pi \epsilon _0 \times 10 r$
$\therefore$ Potential of the big drop 
=$\displaystyle \frac{1000}{10} . \frac{q}{4 \pi \epsilon _0 r} =100V$

A circuit contains a capacitor and inductance each with negligible resistance. The capacitor is initially charged and the charging battery is disconnected. At subsequent time, the charge on the capacitor will 

capacitance of an isolated spherical conductor capacitance of isolated bodies capacitance physics

  1. Increase exponentially

  2. Decrease exponentially

  3. Decrease linearly

  4. Remain constant

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Correct Option: D

A fully charged capacitor has a capacitance C.It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity s and mass m. If the temperature of the block is raised by $\Delta T$, the potential difference V across the capacitance is:

capacitance of an isolated spherical conductor capacitance of isolated bodies capacitance physics

  1. ${{ms\Delta T} \over C}$

  2. $\sqrt {{{ms\Delta T} \over C}} $

  3. $\sqrt {{{2ms\Delta T} \over C}} $

  4. ${{ms\Delta T} \over s}$

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Correct Option: C
Explanation:

The electric potential energy stored in capacitor is $=\cfrac{CV^2}{2}$

This energy is dissipated in the circuit through the resistance wire. The heat is absorbed by th einsulated block. Apply conservation of energy
Heat absorbed $=ms\Delta T=CV^2/2$
$\Rightarrow V=\sqrt{\cfrac{2ms\Delta T}{C}}$

Capacitance of an isolated metallic sphere having radius $8.1$ mm is nearly :

capacitance of an isolated spherical conductor capacitance of isolated bodies capacitance physics

  1. $9 \times 10^{-9}$ $\mu F$

  2. $9 \times 10^{-6}$ $\mu F$

  3. $9 \times 10^{-1}$ $p F$

  4. $9 \times 10^{-5}$ $\mu F$

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Correct Option: D
Explanation:

Given,

$r=8.1mm$

The capacitance of an isolated metallic sphere is given by

$C=4\pi \varepsilon _0 r$

$C=4\times 3.14\times 8.85\times 10^{-12}\times 8.1\times 10^{-3}$

$C=900\times 10^{-13}F$

$C=9\times 10^{-5}\mu F$

The correct option is D.

Two points A and B lying on Y- axis at distances 12.3 cm and 12.5 cm from the origin. The potentials at these points are 56V and 54.8V respectively, then the component of force on a charge of $4\mu C$ placed at A along Y- axis will be

capacitance of an isolated spherical conductor capacitance of isolated bodies capacitance physics

  1. 0.12 N

  2. 48$*{10^{ - 3}}$ N

  3. $24*{10^{ - 4}}N$

  4. $96*{10^{ - 2}}N$

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Correct Option: C

The capacitance of an isolated conducting sphere of radius $R$ is proportional to

capacitance of an isolated spherical conductor capacitance of isolated bodies capacitance physics

  1. $R^{-1}$

  2. $R^{2}$

  3. $R^{-2}$

  4. $R$

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Correct Option: D
Explanation:

The capacity of an isolated spherical conductor of radius $R$ is $4\pi \epsilon _{0}R$
$\therefore C\propto R$.