Numerical Problems Based on Energy in Capacitors for Class 12 Physics
Q.1. A battery of 10 V is connected to a capacitor of capacity 0.1 F. The battery is now removed and this capacitor is connected to a second uncharged capacitor. If the charge distributes equally on these two capacitors, find the total energy stored in the two capacitors. Further, compare this energy with the initial energy stored in the first capacitor.
(Ans. 2.5 J, 1:2)
Q.2. A 10 μF capacitor is charged by a 30 V d.c. supply and then connected across an uncharged 50 μF capacitor. Calculate (i) the final potential difference across the combination, and (ii) the initial and final energies. How will you account for the difference in energy?
[Ans. (i) 5V, (ii) ui = 4.5 ×10-3 J, Uf = 0.75 × 10-3 J]
Q.3. Net capacitance of three identical capacitors in series is 1 μF. What will be their net capacitance if connected in parallel? Find the ratio of energy stored in the two configurations if they are both connected to the same source.
(Ans. 9 μF, 1 : 9)
Q.4. Two capacitors are in parallel and the energy stored is 45 J, when the combination is raised to potential of 3000 V. With the same two capacitors in series, the energy stored is 4.05 J for the same potential. What are their individual capacitances?
(Ans. 9 μF, 1 μF)
Why Students Fear Numerical Problems in Class 12 Physics?
The exam pattern for of previous exams generally consists of straightforward numerical problems that require students to apply basic mathematical concepts to solve problems. However, some common reasons for students’ fear of numerical problems in this class include:
- Lack of practice: Students need to practice solving numerical problems regularly to build their confidence and understanding of the concepts. The exam pattern for Class 10 Science is relatively easy, but students need to ensure they are well-prepared for the exam by practicing regularly.
- Fear of making mistakes: Since the exam pattern for Class 10 Science includes numerical problems, students may fear making mistakes while solving problems. Teachers should encourage students to understand the problem statement carefully and double-check their calculations to minimize errors.
- Lack of conceptual clarity: Students may struggle with numerical problems if they do not have a clear understanding of the concepts involved. Teachers should ensure that students understand the fundamental concepts related to numerical problems to avoid confusion.
- Difficulty in understanding the problem: Sometimes, students may struggle to understand the problem statement or may not know which formula to use. Teachers should guide students on how to identify the correct formula and approach to solve numerical problems.
How to Prepare for Numerical Problems in Class 12 Physics?
Here are some tips for effective preparation:
- Build a Strong Foundation: Students should ensure that they have a clear understanding of the underlying concepts involved in numerical problems. They should review their notes regularly and seek clarification from teachers if they have any doubts.
- Practice Regularly: Solving numerical problems regularly is crucial to build confidence and improve problem-solving skills. Students should practice a variety of problems to develop their understanding of different concepts and formulas.
- Focus on Understanding: Instead of rote memorization, students should focus on understanding the steps involved in solving numerical problems. This approach will help them tackle more complex problems.
- Check for Mistakes: After solving numerical problems, students should double-check their calculations and identify any mistakes. This practice will help them avoid making careless errors and increase their accuracy.
- Seek Help: If students are struggling with a particular concept or problem, they should seek help from teachers, tutors, or classmates. Clarifying doubts early on can prevent confusion and frustration later.
- Mock Tests: Mock tests can help students assess their preparedness and identify areas for improvement. Students should take mock tests regularly and analyze their performance to identify weak areas.