Introduction:
Solving numerical problems without using calculators can be beneficial for electrical engineering students. It helps in developing a strong understanding of the concepts, enhancing problem-solving skills, and promoting critical thinking. However, there are certain factors to consider before deciding whether to solve numerical problems without calculators or not.

Benefits of solving without calculators:
1. Conceptual understanding: Solving numerical problems manually allows students to grasp the underlying concepts more effectively. It enables them to visualize the steps involved in calculations and gain a deeper understanding of the principles involved.

2. Problem-solving skills: By solving problems manually, students can improve their problem-solving abilities. They learn to break down complex problems into smaller, manageable steps, identify relevant formulas or equations, and apply them effectively.

3. Accuracy: Relying solely on calculators may lead to errors if input data or calculations are not entered correctly. Manual calculations provide an opportunity to double-check the results and ensure accuracy.

4. Real-life scenarios: In real-life scenarios, engineers often need to perform quick calculations without relying on calculators. Developing the ability to solve problems manually equips students with the necessary skills for such situations.

5. Exam preparation: Many exams, including the UPSC, may restrict the use of calculators. Therefore, practicing without calculators helps students become familiar with the exam conditions and perform better in the actual test.

Limitations:
1. Time-consuming: Manual calculations can be time-consuming, especially for complex problems that involve lengthy calculations. The use of calculators can save time in such cases.

2. Complex calculations: Some calculations in electrical engineering involve large numbers, exponentiations, or trigonometric functions, which can be challenging to perform manually. In such cases, calculators can be useful for obtaining accurate results quickly.

3. Focus on problem-solving: In certain situations, the focus may be more on the problem-solving approach rather than the actual calculations. In such cases, calculators can be used to expedite the process and focus on the analysis and interpretation of results.

Conclusion:
In conclusion, solving numerical problems without calculators can be beneficial for electrical engineering students in terms of conceptual understanding, problem-solving skills, accuracy, and real-life scenarios. However, it is essential to consider the complexity of calculations, time constraints, and the specific requirements of exams or real-life situations. Striking a balance between manual calculations and the use of calculators can lead to a well-rounded skill set that is essential for success in the field of electrical engineering.