Question

a capacitor connected to a 10v battery colects a charge of 40microcolumb in air as dielectric and 100 microcolumb wita a given oil as dielectric. the dielectric constant of oil is

Answer 1

I hope no explanation is needed with this picture

Answer 2

Answer:

The dielectric constant of oil is 2.5.

Explanation:

Given that,

Voltage = 10 v

Charge in air $q = 40\times10^{-6}\ C$

Charge in dielectric $q=100\times10^{-6}\C$

The formula of charge

$q =\dfrac{C}{V}$

Where, q = charge

C = capacitor

V = voltage

So, The capacitance is

$C =q\times V$

$C = 40\times10^{-6}\times10$

$C = 40\times10^{-5}\ C$

Now the new capacitance is

$C' =q\times V$

$C' = 100\times10^{-6}\times10$

$C' = 1\times10^{-3}\ C$

Now the capacitance in air

$C= \dfrac{\epsilon_{0} A}{d}$....(I)

For dielectric

$C'= \dfrac{k\epsilon_{0} A}{d}$....(II)

On dividing equation (I) by equation (II)

$\dfrac{C}{C'}=\dfrac{1}{k}$

$\dfrac{40\times10^{-5}}{1\times10^{-3}}=\dfrac{1}{k}$

$k= 2.5$

Hence, The dielectric constant of oil is 2.5.