Answer

Verified

342.6k+ views

**Hint:**It is given in the question that the four metallic plates each with a surface area of A placed at a distance d from each other and we have to find the capacitance between point a and b to do so we have to simplify the given figure and check which the capacitor is parallel to the each other and which one is in series and by using formula of the capacitance we can get total capacitance of the given system.

**Formula used:**

$C=\dfrac{{{\varepsilon }_{o}}A}{d}$

**Complete answer:**

In order to find a solution we have to simplify the circuit by making all four plates by 1, 2, 3, and 4 as shown in the figure.

Now to further simplify the circuit we will write points step by step and then we will draw full circuit.

Now ‘a’ is connected with the plate 2 which is in connection with the plate 1 and the plate 3, therefore capacitor 21 and 23 will be in parallel connection.

Now plate 1 is connected to plate 4 which is making a capacitor with plate 3 therefore the capacitor 21 and 43 will be in the series connection.

Now the capacitor with the plate 23 and the plate 43 has common plate 3 which is connected to b.

Now let’s make the figure according to our simplification.

Now the total capacitance of the capacitor which are connected in series is,

Note that all have the same capacitance ‘c’ because their area and the distance are same.

$\begin{align}

& \dfrac{1}{{{C}_{1}}}=\dfrac{1}{C}+\dfrac{1}{C}\text{ }\left( \text{for the plate }\!\!'\!\!\text{ 21 }\!\!'\!\!\text{ and }\!\!'\!\!\text{ 43 }\!\!'\!\!\text{ } \right) \\

& \dfrac{1}{{{C}_{1}}}=\dfrac{2C}{{{C}^{2}}} \\

& \therefore {{C}_{1}}=\dfrac{C}{2}....\left( 1 \right) \\

\end{align}$

Now the total capacitance,

$\begin{align}

& {{C}_{T}}=C+\dfrac{C}{2} \\

& {{C}_{T}}=\dfrac{3C}{2}...\left( 2 \right) \\

\end{align}$

Now we know that formula for the capacitor is,

$C=\dfrac{{{\varepsilon }_{o}}A}{d}$

$C=\dfrac{{{\varepsilon }_{o}}A}{d}$

Where, ${{\varepsilon }_{o}}$ = permittivity

A = area

d = distance between the two conductive plate,

Now substitute value of the equation (3) in the equation (2)

$\begin{align}

& {{C}_{T}}=\dfrac{3}{2}\times \dfrac{{{\varepsilon }_{o}}A}{d} \\

& {{C}_{T}}=\dfrac{3{{\varepsilon }_{o}}A}{2d} \\

\end{align}$

**Therefore the option (D) is correct.**

**Note:**

While calculating capacitance of the parallel circuit and the series circuit be careful while putting the formulas of the series and parallel connection because sometimes we can be mistaken formulas as we are using formulas resistance formula i.e.

Series connection,

Resistance,

${{R}_{e}}={{R}_{1}}+{{R}_{2}}+{{R}_{3}}....$

Capacitor,

$\dfrac{1}{{{C}_{e}}}=\dfrac{1}{{{C}_{1}}}+\dfrac{1}{{{C}_{2}}}+\dfrac{1}{{{C}_{3}}}....$

Parallel connection,

Resistance,

$\dfrac{1}{{{R}_{e}}}=\dfrac{1}{{{R}_{1}}}+\dfrac{1}{{{R}_{2}}}+\dfrac{1}{{{R}_{3}}}......$

Capacitor,

${{C}_{e}}={{C}_{1}}+{{C}_{2}}+{{C}_{3}}.....$

Recently Updated Pages

Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred

Basicity of sulphurous acid and sulphuric acid are

The branch of science which deals with nature and natural class 10 physics CBSE

What is the stopping potential when the metal with class 12 physics JEE_Main

The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main

How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Draw a diagram of nephron and explain its structur class 11 biology CBSE

What is the color of ferrous sulphate crystals? How does this color change after heating? Name the products formed on strongly heating ferrous sulphate crystals. What type of chemical reaction occurs in this type of change.

Write the difference between soap and detergent class 10 chemistry CBSE

Give 10 examples of unisexual and bisexual flowers

Differentiate between calcination and roasting class 11 chemistry CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

What is the difference between anaerobic aerobic respiration class 10 biology CBSE

a Why did Mendel choose pea plants for his experiments class 10 biology CBSE