Question

The amount of work done in increasing the voltage across the plates of capacitor from 5 V to 10 V is W. The work done in increasing it from 10 V to 15 V will be ______.

Options

• W 

• 0.6 W

• 1.25 W

• 1.67 W

Answer 1

The amount of work done in increasing the voltage across the plates of capacitor from 5 V to 10 V is W The work done in increasing it from 10 V to 15 V will be 1.67 W.

Explanation:

Work done in increasing the voltage from v₁ to v₂ is given by

= `1/2"C"("V"_2^2-"V"_1^2)`

putting the values, we get

= `1/2xx"C"xx(10^2-5^2)`

W = `1/2xx"C"xx75`

= `(75"C")/2`                 ...(i)

Again work done when the plate voltage is increased from 10 V to 15 V is given by

W₁ = `1/2xx"C"xx(15^2-10^2)`

⇒ W₁ = `1/2xx"C"xx125`

= `(125"C")/2`             ...(ii)

Using eqs. (i) and (ii), we get

`"W"/"W"_1=(75"C")/(2xx125"C")xx2`

⇒ `"W"_1/"W"=125/75=5/3`

⇒ W₁ = 1.67 W