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

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

  1. 10 V

  2. 100 V

  3. 1000V

  4. $\displaystyle \frac{V}{100}$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 
=$\displaystyle \frac{1000}{10} . \frac{q}{4 \pi \epsilon _0 r} =100V$

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

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:

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

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

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

  4. ${{ms\Delta T} \over s}$
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $=ms\Delta T=CV^2/2$
$\Rightarrow V=\sqrt{\cfrac{2ms\Delta T}{C}}$

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

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

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

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

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

  4. $9 \times 10^{-5}$ $\mu F$
Reveal answer Fill a bubble to check yourself
D Correct answer
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.

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

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

  1. 0.12 N

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

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

  4. $96*{10^{ - 2}}N$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Electric field E = -dV/dy = -(54.8 - 56) / (12.5 - 12.3) = -(-1.2) / 0.2 = 6 V/cm = 600 V/m. Force F = qE = 4 * 10^-6 * 600 = 24 * 10^-4 N.

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

Two metal spheres of capacitance, ${C} _{1}$ and ${C} _{2}$ carry some charges. They are put in contact and then separated. The final charges ${Q} _{1}$ and ${Q} _{2}$ on them will satisfy:

  1. $\dfrac { { Q } _{ 1 } }{ { Q } _{ 2 } } <\dfrac { { C } _{ 1 } }{ { C } _{ 2 } }$

  2. $\dfrac { { Q } _{ 1 } }{ { Q } _{ 2 } } =\dfrac { { C } _{ 1 } }{ { C } _{ 2 } }$

  3. $\dfrac { { Q } _{ 1 } }{ { Q } _{ 2 } } >\dfrac { { C } _{ 1 } }{ { C } _{ 2 } }$

  4. $\dfrac { { Q } _{ 1 } }{ { Q } _{ 2 } } =\dfrac { { C } _{ 2 } }{ { C } _{ 1 } }$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the charge on two sphere initially are $q _1\ &\ q _2$. Now when these two capacitors (spheres) are kept in contact with each other and separated. Then charges on the two spheres are,


Let $Q _1\ &\ Q _2$ are the final charges on spheres. So, final charge will be conserved.
$Q _1+Q _2=q _1+q _2$

$\dfrac{Q _1}{Q _2}=\dfrac{C _1V _1}{C _2V _2}$

The charge will flow until the potential of both the spheres becomes the same.
$\dfrac{Q _1}{Q _2}=\dfrac{C _1V}{C _2V}$

$\dfrac{Q _1}{Q _2}=\dfrac{C _1}{C _2}$

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

Three capacitors of capacitances 6 µF each are available. The minimum and maximum capacitances, which may be obtained are

  1. $ 2 \mu F $ and $ 18 \mu F $

  2. $ 5 \mu F $ and $ 5 \mu F $

  3. $ 7 \mu F $ and $ 3 \mu F $

  4. $ 8 \mu F $ and $ 2 \mu F $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For three 6 uF capacitors: Series combination C_min = 6/3 = 2 uF. Parallel combination C_max = 6 * 3 = 18 uF.

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

The capacitance of a spherical condenser is $1mF$. If the spacing between the two spheres is $1mm$, then the radius of the outer sphere is

  1. $30cm$

  2. $6m$

  3. $5cm$

  4. $3m$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\begin{array}{l} From\, \, the\, question \\ C=\dfrac { { 4\pi { \varepsilon _{ 0 } } } }{ { \left[ { \dfrac { 1 }{ { { r _{ in } } } } -\dfrac { 1 }{ { { r _{ out } } } }  } \right]  } } =\dfrac { { 4\pi \varepsilon  } }{ { \left[ { \dfrac { 1 }{ { { r _{ 1 } } } } -\dfrac { 1 }{ { { r _{ 1 } }+0.001 } }  } \right]  } }  \\ 1\times { 10^{ -6 } }=\dfrac { { 4\times 3.14\times 8.854\times { { 10 }^{ -12 } } } }{ { \left[ { \dfrac { 1 }{ { { r _{ 1 } } } } -\dfrac { 1 }{ { { r _{ 1 } }+0.001 } }  } \right]  } }  \\ \left[ { \dfrac { 1 }{ { { r _{ 1 } } } } -\dfrac { 1 }{ { { r _{ 1 } }+0.001 } }  } \right] =\dfrac { { 4\times 3.14\times 8.854\times { { 10 }^{ -12 } } } }{ { 1\times { { 10 }^{ -6 } } } }  \\ \dfrac { { \left[ { \left( { { r _{ 1 } }+0.001 } \right) -{ r _{ 1 } } } \right]  } }{ { { r _{ 1 } }\times \left( { { r _{ 1 } }+0.001 } \right)  } } =4\times 3.14\times 8.854\times { 10^{ -6 } } \\ { r _{ 1 } }\times \left( { { r _{ 1 } }+0.001 } \right) =\dfrac { { 4\times 3.14\times 8.854\times { { 10 }^{ -6 } } } }{ { 0.001 } }  \\ r _{ 1 }^{ 2 }+0.001{ r _{ 1 } }-4\times 3.14\times 8.854\times { 10^{ -3 } }=0 \\ r _{ 1 }^{ 2 }+0.001{ r _{ 1 } }-0.1112=0 \\ { r _{ 1 } }=0.333m\, \, \, or\, \, { r _{ 1 } }=-334m \\ Since,\, it\, cannot\, be\, negative \\ Thereforem\, radius\, \, of\, outer\, \, sphere\, ={ r _{ 1 } }+0.001 \\ { r _{ outer } }=0.334m \\ or,\, { r _{ 1 } }=33.4cm \\  \end{array}$

Hence, the option $A$ is the correct answer.