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Quizzes (598) Questions (13441)

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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 space is

  1. $30cm$

  2. $6m$

  3. $5cm$

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

$\begin{array}{l} C=\frac { { 4\pi { E _{ 0 } } } }{ { \left( { \frac { 1 }{ { { r _{ i } } } }  } \right) -\left( { \frac { 1 }{ { { r _{ 0 } } } }  } \right)  } } .....................\left( 1 \right)  \ According\, \, to\, \, the\, \, question:- \ { r _{ 0 } }-{ r _{ 1 } }=0.001\, m \ C=0.00000\, 1F..............\left( 2 \right)  \ Putting\, \, \left( 2 \right) \, \, in\, \, \, \left( 1 \right)  \ \therefore r _{ 0 }^{ 2 }-{ r _{ 0 } }\left( { 0.001 } \right) -\left( { 9\times 000000000\times 0.000000001 } \right) =0 \ therefore\, \, { r _{ 0 } }=3\, \, m \end{array}$

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

A capacitor has capacitance $2F$. plate separation $0.5 cm $ then area of plate  [You will realize from your answer why ordinary capacitors are in the range of μF or less. However, electrolytic capacitors do have a much larger capacitance $(0.1 F)$ because of very minute separation between the conductors.]:

  1. $1130cm^2$

  2. $1130m^2$

  3. $1130km^2$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

C = epsilon_0 * A / d. A = C * d / epsilon_0 = 2 * 0.005 / (8.85 * 10^-12) = 1.13 * 10^9 m^2 = 1130 km^2.

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

A coil, a capacitor and an A. C. source of rms voltage 24 V are connected in series. By varying the frequency of the source, a maximum rms current of 6 A is observed. If the coil is connected to a battery of emf 12 V and internal resistance $4\Omega$, the current through it will be    

  1. 2.4 A

  2. 1.8 A

  3. 1.5 A

  4. 1.2 A
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\begin{array}{l} { E _{ rms } }=24V \ r=4\Omega ,\, \, \, { I _{ rms } }=6A \ R=\frac { E }{ I } =\frac { { 24 } }{ 6 } =4\Omega  \ Internal\, { { Re } }sis\tan  ce=4\Omega  \ Hence,\, net\, resis\tan  ce=4+4=8\Omega  \ \therefore Current=\frac { { 12 } }{ 8 } =1.5A \  \end{array}$

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

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

The capacitance (C) for an isolated conducting sphere of radius(a) is given by $4\pi \varepsilon _0a$. If the sphere is enclosed with an earthed concentric sphere, the ratio of the radii of the spheres being $\dfrac{n}{(n-1)}$ then the capacitance of such a sphere will be increased by a factor?

  1. $n$

  2. $\dfrac{n}{(n-1)}$

  3. $\dfrac{(n-1)}{n}$

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

Capacitance of isolated sphere C1 = 4 * pi * epsilon_0 * a. Capacitance of spherical capacitor C2 = 4 * pi * epsilon_0 * a * b / (b - a). Given b/a = n/(n-1), then b = a * n / (n-1). Substituting gives C2 = C1 * n.

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

If the circumferences of a sphere is $2\ m$, then capacitance of sphere in water would be:

  1. $2700\ pF$

  2. $2760\ pF$

  3. $2780\ pF$

  4. $2846\ pF$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Capacitance is given as

$C=\varepsilon _0\frac{A}{d}$
For a sphere placed in water, the capacitance will be,
$C=4\pi \varepsilon R$
Here, $\varepsilon$ os the permittivity of water 
In terms of permittivity of free space and dielectric constant of water, we get 
$C=4\pi \varepsilon _0kR$
It is given that circumference is 2m
Hence, $c=2\pi R$  
$\therefore R=\frac{1}{\pi}$
$C=4\pi \varepsilon _0k\frac{1}{\pi}=4\varepsilon _0k$
$C=4\times 8.85\times10^{-12}\times80.4$
$C=2846\times 10^{-12}F$
$C=2846 pF$

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

Inside a hollow charged spherical conductor, the electric field is found to be.

  1. Proportional to the distance from the centre

  2. A function of the area of the sphere

  3. Zero

  4. A function of the charge density of the sphere
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

According to Gauss's Law, the electric field inside a hollow charged conductor is zero because there is no enclosed charge.

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

Of the following about capacitive reactance which is correct

  1. the reactance of the capacitor is directly proportional to its ability to store charge

  2. capacitive reactance is inversely proportional to the frequency of the current

  3. capacitive reactance is me sured in farad

  4. the reactance of a capacitor in an A.C circuit is similar to the resistance of a capacitor in a D.C circuit
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice kirchoff's laws black body radiation heat transfer thermal properties physics

If the emissive and absorptive powers of a body are $E$ and $A $ respectively at temperature $T$ then emissive power of a black body will be

  1. $E/A$

  2. $EAT$

  3. $EA/T$

  4. $A/E$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If Emissive power =$ E$
Absorptive power = $A$
The emissive power of a black body is the emissive power for unit absorptive power(per unit absorptive power) (Black body absorbs all radiations)  = $\dfrac{E}{A}$

Multiple choice kirchoff's laws black body radiation heat transfer thermal properties physics

If $p$ calories of heat energy is incident on a body and $q$ calories is absorbed, then its coefficient of absorption is :

  1. $\dfrac{p}{q}$

  2. $p - q$

  3. $\dfrac{q}{p}$

  4. $q + p$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Calories of incident heat=$p$
Calories of absorbed heat=$q$
$\because$ we know that coefficient of absorption is the ratio of heat absorbed to the incident heat.
So, coefficient of absorption=$\cfrac{q}{p}$