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  • A capacitor filled with an insulator and a certain potential difference is applied to the plates. The energy stored in the capacitor is  <img alt="U" src="https://entrancecorner.oncodecog

A capacitor filled with an insulator and a certain potential difference is applied to the plates. The energy stored in the capacitor is  U. If the capacitor is disconnected from the source and the insulator is pulled out of the capacitor then what is the dielectric constant, if the work performed against the forces of electric field in pulling out the insulator is 2 U.

Option: 1

3
 


Option: 2

4
 


Option: 3

5
 


Option: 4

8


Answers (1)

best_answer

The capacitor originally had the energy \mathrm{U} and the work required to pull the insulator out is 2 \mathrm{U} so the final energy is equal to 3 \mathrm{U}

U_f=2 U+U=3 U      .........(1)

The capacitance of the insulator with an insulator,

\Rightarrow C=\frac{A \varepsilon_o}{d} \cdot k \ldots \ldots . \text { eq. (2) }

The energy of the insulator is given by,

\Rightarrow U=\frac{q^2}{2 C} \ldots \ldots \text { eq. (3) }

When we remove the insulator from the capacitor then the capacitance gets \mathrm{C}_0 which will be to, 

\Rightarrow C_o=\frac{A \cdot \varepsilon_o}{d} \ldots \ldots \text { eq. (4) }

And the stored energy will be,

\Rightarrow U_f=\frac{q^2}{2 C_o} \ldots \ldots \text {.... (5) }

Since,

U_f=3 U

Replacing the value of  U and  U_f in the above equation from the equation (3) and equation (5) we get

\begin{gathered} U_f=3 U \\ O r, \frac{q^2}{2 C_o}=3 \frac{q^2}{2 C} \\ \text { Or, } \frac{1}{C_o}=\frac{3}{C} \\ O r, \frac{C}{C_o}=3 \end{gathered}

Replacing the value of C and C_0  in the above relation from equation (2) and equation (4) we get. 

\begin{gathered} \frac{C}{C_o}=3 \\ O r, \frac{\frac{A \epsilon_o}{d} k}{\frac{A \epsilon_o}{d}}=3 \\ O r, k=3 \end{gathered}

The dielectric constant value is equal to k=3

 

Posted by

Sanket Gandhi

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