Q179 / 180 · COMEDK 2015 · Physics

A parallel plate capacitor has a capacity $C$. The separation between the plates is doubled and a dielectric medium is inserted between the plates. If the capacity is $3 C$, then the dielectric constant of the medium will be

  • A
    $1.5$
  • B
    $3$
  • Correct answer
    C
    $6$
  • D
    $12$

Solution

We know that, capacitance of a parallel plate capacitor, $$ C=\frac{\varepsilon_{0} A}{d} $$ where, $A=$ area of plate $d=$ separation between the plates. When $d^{\prime}=2 d$, then $C^{\prime}=\frac{\varepsilon_{0} A K}{d^{\prime}}$ $\Rightarrow \quad 3 C=\frac{\varepsilon_{0} A K}{2 d}$ $\left[\because C^{\prime}=3 C\right]$ $\Rightarrow \quad 3 C=\frac{\varepsilon_{0} A}{d} \cdot \frac{K}{2}$ $\Rightarrow \quad 3 C=C \cdot \frac{K}{2} \quad$ [from Eq. (i)] $\Rightarrow \quad 3=\frac{K}{2}$ $\Rightarrow \quad K=6$

Hence, the correct answer is option: 'C'.

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