Tag: capacitance

Questions Related to capacitance

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

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

  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

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Correct Option: C

Of the following about capacitive reactance which is correct

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

  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

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Correct Option: A

Two capacitors of $1\mu F$ and $2\mu F$ are connected in series and this combination is changed upto a potential difference of $120$ volt. What will be the potential difference across $1 \mu F$ capacitor:

physics capacitance capacitors in series combination of capacitors capacitors in parallel and series

  1. $40 volt$

  2. $60 volt$

  3. $80 volt$

  4. $120 volt$

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Correct Option: C
Explanation:
Given, $c _1=1\mu f,c _2=2\mu f,PD=120v$

$C _{eq}=\dfrac{c _1c _2}{c _1+c _2}=\dfrac{2\times1}{2+1}=\dfrac{2}{3}\mu f$

We know,  $Q=cv$ Where Q is the charge, C is the capacitance of the capacitor and v is the potential difference.

Now, $Q _{net}$ in circuit is equivalent capacitance of capacitors attached in the circuits is multiplied by PD

$Q _{net}=12\times\dfrac{2}{3}=80$

$Q=cv=1\mu fv=80\Rightarrow v=80v$

Three long concentric cylindrical shells have radii R, 2R and $2\sqrt{2}R$. Inner and outer shells are connected to each other. The capacitance across middle and inner shells per unit length is:

physics capacitance capacitors in series combination of capacitors capacitors in parallel and series

  1. $\dfrac{\dfrac{1}{3}\epsilon _0}{ln 2}$

  2. $\dfrac{6\pi \epsilon _0}{ln 2}$

  3. $\dfrac{\pi \epsilon _0}{2 ln 2}$

  4. None

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Correct Option: B

Six identical square metallic plates are arranged as shown in figure length of each plate is l the capacitance of this arrangement should be

physics capacitance capacitors in series combination of capacitors capacitors in parallel and series

  1. $3\epsilon _0l^2/d$

  2. $4\epsilon _0l^2/d$

  3. $3\epsilon _0l^2/2d$

  4. $2\epsilon _0l^2/d$

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Correct Option: A

Two capacitors of caacity ${ C } _{ 1 }$ and ${ C } _{ 2}$ are connected in series and potential difference V is applied across it. Then the potential difference across${ C } _{ 1 }$ will be 

physics capacitance capacitors in series combination of capacitors capacitors in parallel and series

  1. $V\frac { { C } _{ 2 } }{ { C } _{ 1 } } $

  2. $V\frac { { C } _{ 1 }+{ C } _{ 2 } }{ { C } _{ 1 } } $

  3. $V\frac { { C } _{ 2 } }{ { C } _{ 1 }+{ C } _{ 2 } } $

  4. $V\frac { { C } _{ 1 } }{ { C } _{ 1 }+{ C } _{ 2 } } $

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Correct Option: A

For capacitors in the series combination, the total capacitance C is given by

physics capacitance capacitors in series combination of capacitors capacitors in parallel and series

  1. $C=(\cfrac{1}{C _1}+\cfrac{1}{C _2} + ......)$

  2. $C = C _{1} + C _{2} +$ .......

  3. $\cfrac{1}{C}=(\cfrac{1}{C _1}+\cfrac{1}{C _2}+.....)$

  4. $\cfrac{1}{C} = C _{1} + C _{2} +$ ........

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Correct Option: C
Explanation:

When in series, the reciprocal of the net capacitance is equal to the sum of reciprocal of individual capacitances.

A series combination of two capacitances of value $0.1\ mu F$ and $1\mu F$ is connected with a source of voltage $500\ volts$. The potential difference in volts across the capacitor of value $0.1\ muF$ will be :

physics capacitance capacitors in series combination of capacitors capacitors in parallel and series

  1. $50$

  2. $500$

  3. $45.5$

  4. $454.5$

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Correct Option: D
Explanation:

Given,

Capacitance, ${{C} _{1}}=0.1\,\mu F\,\,and\,\,{{C} _{2}}=1\,\mu F$

In series charge is equal

$ Q={{C} _{1}}{{V} _{1}}={{C} _{2}}{{V} _{2}} $

$ {{V} _{2}}=\dfrac{{{C} _{1}}{{V} _{1}}}{{{C} _{2}}} $

In series total potential difference is sum of all paternal difference

$ V={{V} _{1}}+{{V} _{2}} $

$ V={{V} _{1}}+\dfrac{{{C} _{1}}{{V} _{1}}}{{{C} _{2}}}={{V} _{1}}\left( \dfrac{{{C} _{2}}+{{C} _{1}}}{{{C} _{2}}} \right) $

$ {{V} _{1}}=\dfrac{{{C} _{2}}V}{{{C} _{2}}+{{C} _{1}}}=\dfrac{1\times 500}{1+0.1}=454.54\,V $

Hence, Potential difference across $0.1\,\mu F\,\,\,is\,\,\,454.5\,V$ 

Two parallel plate capacitors are connected in series. Each capacitor has a plate area A and a separation d between the plates. The dielectric constant of the medium between their plates are 2 and 4 . The separation between the plates of a single air capacitors of plate area A which effectively replaces the combination is:

physics capacitance capacitors in series combination of capacitors capacitors in parallel and series

  1. 2d/3

  2. 3d/2

  3. 3d/4

  4. 8d/5

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Correct Option: B

A capacitor comprises of two parallel circular plates. Diameter of each of plates is equal to $6 cm$. If capacitance of above system is equivalent to capacitance of sphere, whose diameter is equal to $200 cm$. Distance between two plates will be:-

physics capacitance capacitors in series combination of capacitors capacitors in parallel and series

  1. $2.25 \times 10^{-4} m$

  2. $4.5 \times 10^{-4} m$

  3. $6.75 \times 10^{-4} m$

  4. $9 \times 10^{-4} m$

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Correct Option: B