A parallel plate capacitor is formed by two plates each of area 30πcm² separated by 1 mm. A material of dielectric strength 3.6 × 10⁷ Vm^-¹ is filled between the plates. If the maximum charge that can be stored on the capacitor without causing any dielectric breakdown is 7 × 10^-⁶ C, the value of dielectric constant of the material is [Use ] $\frac{1}{4 π ε_{0}} = 9 \times 1 0^{9} N m^{2} C^{- 2}$

Option 1 -

1.66

Option 2 -

1.75

Option 3 -

2.25

Option 4 -

2.33

2 Views | Posted 3 months ago

Asked by Shiksha User

1 Answer

Answered by

Vishal Baghel | Contributor-Level 10

3 months ago

Correct Option - 4

Detailed Solution:

A = 30p cm² = 30p × 10^-⁴ m²

d = 1mm = 10^-³ m

E = (dielectric strength for breakdown)

= 3.6 × 10⁷ v/m

Q = 7 × 10^-⁶C

$\frac{σ}{\in_{0}} = E$

$\Rightarrow \frac{Q}{k A \in_{0}} = E$

$k = \frac{Q}{A \in_{0} E}$

$= \frac{7 \times 1 0^{- 6} \times 4 π \times 9 \times 1 0^{9}}{30 π \times 1 0^{- 4} \times 1 \times 3.6 \times 1 0^{7}}$

$= \frac{7 \times 4 π \times 9}{30 π \times 3.6}$

$= \frac{7 \times 4 \times 9 \times 10}{30 \times 36}$

$= \frac{70}{30}$

$k = \frac{7}{3} = 2.33$

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