Chemistry, asked by vatsavaibhav132, 3 days ago

A parallel plate air capacitor is charged to 50 V and is then connected to an uncharged geometrically identical capacitor in parallel. The second capacitor has some dielectric medium between its plates. If the common potential is 10 V, the dielectric constant of the medium is

Answers

Answered by javediqbal956r
7

Answer:

then the potential remain same it becomes zero at the charged parallel plate, capacitor

Answered by talasilavijaya
5

Answer:

The dielectric constant of the medium is 4.

Explanation:

Common potential:

  • When two capacitors charged at different potentials are connected in parallel with each other, the charge flows from a capacitor at higher potential to the capacitor at lower potential till an equal potential, called common potential is obtained.
  • The common potential is given by

        V=\dfrac{C_1V_1+C_2V_2}{C_1+C_2}

  • where C is the capacitance and V is the potential.

Capacitance:

  • The capacitance of a parallel plate capacitor is given by:

        C=k\varepsilon_0 \dfrac{A}{d}

  • where \varepsilon_0=8.854 \times 10^{-12} F/m is the permittivity of free space, k is the dielectric constant of the medium, d is the separation between the plates and A is the area of plates.

Given the potential of  parallel plate air capacitor, V_1=50 V

Capacitance of parallel plate air capacitor, for k = 1,

C_1=\varepsilon_0 \dfrac{A}{d}

The potential of  parallel plate capacitor with dielectric, V_2=0 V

Capacitance of parallel plate capacitor with dielectric,

C_2=k\varepsilon_0 \dfrac{A}{d}

The common potential, V= 10 V

Given both the capacitors are geometrically identical, hence A and d are same.

Substituting the given values in the formula of common potential,

10=\dfrac{\varepsilon_0 \dfrac{A}{d}\times 50+k\varepsilon_0 \dfrac{A}{d}\times 0}{\varepsilon_0 \dfrac{A}{d}+k\varepsilon_0 \dfrac{A}{d}}

\implies 10=\dfrac{\varepsilon_0 \dfrac{A}{d}\times 50}{\varepsilon_0 \dfrac{A}{d}(1+k)}=\dfrac{50}{1+k}

\implies 10(1+k)=50\implies 1+k=\dfrac{50}{10} =5

\implies k=5-1=4

Therefore, the dielectric constant of the medium is 4.

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