Tag: physics

Questions Related to 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

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

  1. 10 V

  2. 100 V

  3. 1000V

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

Show answer
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

Show answer
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. ${{ms\Delta T} \over s}$

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

Show answer
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. $96*{10^{ - 2}}N$

Show answer
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. $R$

Show answer
Correct Option: D
Explanation:

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

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:

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

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

Show answer
Correct Option: B
Explanation:

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


Let $Q _1\ &amp;\ Q _2$ 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.
$\dfrac{Q _1}{Q _2}=\dfrac{C _1V}{C _2V}$

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

A $110V. 60W$ lamp is run from a $220V$ AC mains using a capacitor in series with the lamp, instead of a resistor then the voltage across the capacitor is about:

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

  1. $110V$

  2. $190V$

  3. $220V$

  4. $311V$

Show answer
Correct Option: B
Explanation:
$V _c=\sqrt{V^2-V _R^2}$

$=\sqrt{220^2-110^2}$

$=190V$

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

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

  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 $

Show answer
Correct Option: A

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

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

  1. $30cm$

  2. $6m$

  3. $5cm$

  4. $3m$

Show answer
Correct Option: A
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.