Tag: capacitance of an isolated spherical conductor

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Questions Related to capacitance of an isolated spherical conductor

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

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 = $3.0  \ 10 ^4 \ m/s, \pi = 3.14$):

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

  2. $18.8 \times 10^4 m$

  3. $4.5 \times 10^4 m$

  4. $none\ of\ these$
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice capacitance of an isolated spherical conductor capacitance of isolated bodies capacitance physics

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:

  1. $12.0$

  2. $10.0$

  3. $8.0$

  4. $4.2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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

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

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

  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
Reveal answer Fill a bubble to check yourself
A,C,D Correct answer
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.