SATHEE: Electrostatics 5 Question 13

Electrostatics 5 Question 13

14. A parallel plate capacitor having capacitance $12 pF$ is charged by a battery to a potential difference of $10 V$ between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant 6.5 is slipped between the plates. The work done by the capacitor on the slab is

(a) $560 pJ$

(b) $508 pJ$

(d) $600 pJ$

Show Answer

Answer:

Correct Answer: 14. (b)

Solution:

Energy stored in a charged capacitor is given by

$U = \frac{1}{2} C V^{2} = \frac{1}{2} \cdot \frac{Q^{2}}{C}$

Here, $C = 12 \times 10^{- 12} F$ and $V = 10 V$ .

$\begin{aligned} \Rightarrow U & = \frac{1}{2} \times 12 \times 10^{- 12} \times 100 \\ U & = 6 \times 10^{- 10} J \end{aligned}$

After insertion of slab, capacitance will be

$C^{'} = K C and final energy,$

$\begin{aligned} U^{'} & = \frac{1}{2} \cdot \frac{Q^{2}}{C^{'}} = \frac{1}{2} \frac{Q^{2}}{K C} \\ \Rightarrow U^{'} & = \frac{1}{K} U = \frac{1}{6.5} \times 6 \times 10^{- 10} J \end{aligned}$

So, energy dissipated in the process will be equal to work done on the slab, i.e.

$\begin{aligned} Δ U & = U - U^{'} = 1 - \frac{1}{6.5} \times 6 \times 10^{- 10} J \\ \Rightarrow Δ U & = \frac{5.5}{6.5} \times 6 \times 10^{- 10} J \\ ≅ 5.08 \times 10^{- 10} J or 508 pJ \end{aligned}$

Electrostatics 5 Question 13

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Electrostatics 5 Question 13

14. A parallel plate capacitor having capacitance 12pF is charged by a battery to a potential difference of 10 V between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant 6.5 is slipped between the plates. The work done by the capacitor on the slab is

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu