A leaky parallel capacitor is filled completely with a material having dielectric constant K-5 and electrical conductivity -7-4- 10-12-1m-1- Charge on the plate at instant t-0 is q-8-885 - C- Then time constant of leaky capacitor is -

The correct option is B 6 sParallel plate capacitance with dielectric #160; C=AKϵ_0d #160;where A= area of plates and d= separation betwe ...

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Byju's Answer

Standard XII

Physics

Capacitance of Parallel Plate Capacitor

A leaky paral...

Question

A leaky parallel capacitor is filled completely with a material having dielectric constant $K = 5$ and electrical conductivity $σ = 7.4 \times 10^{- 12} Ω^{- 1} m^{- 1}$ . Charge on the plate at instant $t = 0$ is $q = 8.885 μ C$ . Then time constant of leaky capacitor is :

3 s

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4 s

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5 s

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6 s

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Solution

The correct option is B 6 s
Parallel plate capacitance with dielectric $C = \frac{A K ϵ_{0}}{d}$ where $A =$ area of plates and $d =$ separation between plates.
Time constant $τ = C R$
here, $R = \frac{d}{σ A}$
so $τ = \frac{A K ϵ_{0}}{d} \times \frac{d}{σ A}$
$= \frac{K ϵ_{0}}{σ} = \frac{5 \times 8.85 \times 10^{- 12}}{7.4 \times 10^{- 12}} = 6 s$

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A leaky parallel capacitor is filled completely with a material having dielectric constant K=5 and electrical conductivity σ=7.4×10−12Ω−1m−1. Charge on the plate at instant t=0 is q=8.885μC. Then time constant of leaky capacitor is :

The correct option is B 6 sParallel plate capacitance with dielectric C=AKϵ0d where A= area of plates and d= separation between plates.Time constant τ=CRhere, R=dσAso τ=AKϵ0d×dσA=Kϵ0σ=5×8.85×10−127.4×10−12=6s

A leaky parallel capacitor is filled completely with a material having dielectric constant $K = 5$ and electrical conductivity $σ = 7.4 \times 10^{- 12} Ω^{- 1} m^{- 1}$ . Charge on the plate at instant $t = 0$ is $q = 8.885 μ C$ . Then time constant of leaky capacitor is :