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

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 

  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 } } $
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice physics capacitance capacitors in series combination of capacitors capacitors in parallel and series

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

  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. $\cfrac{1}{C} = C _{1} + C _{2} +$ ........
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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

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

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 :

  1. $50$

  2. $500$

  3. $45.5$

  4. $454.5$
Reveal answer Fill a bubble to check yourself
D Correct answer
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 $0.1\,\mu F\,\,\,is\,\,\,454.5\,V$ 

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

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:

  1. 2d/3

  2. 3d/2

  3. 3d/4

  4. 8d/5
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice physics capacitance capacitors in series combination of capacitors capacitors in parallel and series

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:-

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

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

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

  4. $9 \times 10^{-4} m$
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice physics capacitance capacitors in series combination of capacitors capacitors in parallel and series

Two identical capacitors are connected in series with a source of potential V. If Q is the charge on one of the capacitors, the capacitance of each capacitor is: 

  1. Q/2V

  2. 2Q/V

  3. Q/V

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

In series connection charge on each capacitor would be constant also equivalent capacitance in series $c'=\dfrac{C}{2}$ [ following $\dfrac{1}{c'}=\dfrac{1}{c _1}+\dfrac{1}{c _2}$] and voltage $V$ is applied across it so,from capacitive law,$Q=c'v \Rightarrow Q=\dfrac{CV}{2} \Rightarrow C=\dfrac{2Q}{V}$

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

Two capacitors of $4\ \mu F$and $2\ \mu F$ are connected in series with the battery. If total potential difference across the two capacitors is $200$ volts then the ratio  of potential difference across one capacitor to another is

  1. $1:2$

  2. $2:1$

  3. $1:4$

  4. $4:1$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In series, charge Q is constant. V = Q/C. Therefore, V1/V2 = C2/C1. With C1=4uF and C2=2uF, V1/V2 = 2/4 = 1/2.