SATHEE: electrostatic-potential-and-capacitance Question 40

Electrostatic Potential And Capacitance

electrostatic-potential-and-capacitance Question 40

Question: Q. 11. A $12 p F$ capacitor is connected to a $50 V$ battery. How much electrostatic energy is stored in the capacitor? If another capacitor of $6 p F$ is connected in series with it with the same battery connected across the combination, find the charge stored and potential difference across each capacitor.

U [Delhi II 2017]

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Solution:

Ans. Calculation of electrostatic energy in $12 p F$ capacitor

Total charge stored in combination $1$

Potential difference across each capacitor $1 / 2 + 1 / 2$

Energy stored, in the capacitor of capacitance 12 $p F$ ,

$\begin{aligned} U & = \frac{1}{2} C V^{2} & = \frac{1}{2} \times 12 \times 10^{- 12} \times 50 \times 50 J & = 1.5 \times 10^{- 8} J \end{aligned}$

$C =$ Equivalént capacitance of $12 p F$ and $6 p F$ , in series, is given by

$\begin{aligned} \frac{1}{C} = \frac{1}{12} + \frac{1}{6} = \frac{1 + 2}{12} & C = 4 p F \end{aligned}$

Charge stored across each capacitor

$\begin{aligned} q & = C V & = 4 \times 10^{- 12} \times 50 C & = 2 \times 10^{- 10} C \end{aligned}$

Charge on each capacitor $12 p F$ as well as $6 p F$

$∴$ Potential difference across capacitor $C_{1}$

$\begin{aligned} V_{1} & = \frac{2 \times 10^{- 10}}{12 \times 10^{- 12}} & = \frac{50}{3} V \end{aligned}$

$∴$ Potential difference across capacitor $C_{2}$

$\begin{aligned} ∴ V_{2} = \frac{2 \times 10^{- 10}}{6 \times 10^{- 12}} & = \frac{100}{3} V \end{aligned}$

[CBSE Marking Scheme 2017]

Electrostatic Potential And Capacitance

electrostatic-potential-and-capacitance Question 40

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Electrostatic Potential And Capacitance

electrostatic-potential-and-capacitance Question 40

Table of Contents

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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