Question

A parallel plate of capacitor with air between the plates has a capacitance of 8pF (1pF=10⁻¹² F). What will be the capacitance if the distance between the plates is reduced by half, and the spacebetween them is filled with a substance of dielectric constant ?

Answer 1

Answer:

c= £A/d

distance between plate reduce 1/2 than

c'=£kA/d/2

c'=2k£A/d

c' = 2kc

c'= 16k pF

Answer 2

$\mathfrak{\huge{\red{\underline{Question:-}}}}$

A parallel plate capacitor with air between the plates has a capacitance of 8pF (1pF = 10-12 F). What will be the capacitance if the distance between the plates is reduced by half, and the space between them is filled with a substance of dielectric constant 6?

$\mathfrak{\huge{\red{\underline{Given:-}}}}$

➤ Capacitance = 8pF

➤ Air has dielectric constant = 1

$\mathfrak{\huge{\red{\underline{To \: Find:-}}}}$

➤ Capacitance between the plates.

$\mathfrak{\huge{\red{\underline{Solution:-}}}}$

Given,

Capacitance = 8pF

In first case the parallel plates are at a distance d and is filled with air.

Air has dielectric constant = 1

Capacitance, C = $\sf \dfrac{k \times \epsilon_0 \times A}{d} =\dfrac{\epsilon_0 \times A}{d} \: ... \: eq(1)$

Here,

A = area of each plate

$\sf \epsilon_0=$ permittivity of free space

Now, if the distance between the parallel plates is reduced to half, then

$\sf d_1=d/2$

Given, dielectric constant of the substance,

$\sf k_1=6$

Hence, the capacitance of the capacitor,

$\sf C_1=\dfrac{k_1 \times \epsilon_0 \times A}{d_1}$

$\sf =\dfrac{6 \epsilon_0 \times A}{d/2}$

$\sf =\dfrac{12 \epsilon_0 \: A}{d} \: .... \: (2)$

Taking ratios of eqns. (1) and (2), we get

$\sf C_1 = 2 \times 6 \: C =12 \: C = 12 \times 8 \: pF=\underline{\underline{96 \: pF}}$

Hence, capacitance between the plates is 96 pF.

$\mathfrak{\huge{\red{\underline{Points \: to \: Note:-}}}}$

➤ $\sf Electrostatic \: Potential, \: V = \dfrac{Work \: done, \: W}{Charge, \: q}$

➤ Electrostatic potential is a state dependent function as electrostatic forces are conservative forces.