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How will the capacitance change when 64 spherical conducters of equal size charge potential and capacitance c" each joined together to form a bigger spherical conducter?
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How will the capacitance change when 64 spherical conducters of equal ...
Introduction
When 64 spherical conductors of equal size, each with a capacitance "C", are joined together to form a larger spherical conductor, the overall capacitance changes significantly.
Capacitance of a Single Sphere
- The capacitance "C" of a single spherical conductor is defined as the ability to store charge per unit potential.
Combining Spheres
- When multiple spheres are combined, they effectively create a larger sphere.
- The new capacitance of the larger sphere can be derived from the properties of capacitors in parallel.
Capacitance in Parallel
- For capacitors in parallel, the total capacitance (C_total) is the sum of individual capacitances.
- Therefore, if each of the 64 spheres has a capacitance C, the total capacitance when combined is:
- C_total = 64 * C
Physical Interpretation
- When the smaller spheres unite, they maintain the same potential but can store more charge due to their increased surface area.
- This results in a larger effective capacitance.
Conclusion
- The formation of a larger spherical conductor from 64 smaller spheres increases the overall capacitance to 64 times the capacitance of an individual sphere.
- This principle illustrates how combining conductors enhances their ability to store electrical energy, which is vital in various applications in electrical engineering and physics.
When 64 spherical conductors of equal size, each with a capacitance "C", are joined together to form a larger spherical conductor, the overall capacitance changes significantly.
Capacitance of a Single Sphere
- The capacitance "C" of a single spherical conductor is defined as the ability to store charge per unit potential.
Combining Spheres
- When multiple spheres are combined, they effectively create a larger sphere.
- The new capacitance of the larger sphere can be derived from the properties of capacitors in parallel.
Capacitance in Parallel
- For capacitors in parallel, the total capacitance (C_total) is the sum of individual capacitances.
- Therefore, if each of the 64 spheres has a capacitance C, the total capacitance when combined is:
- C_total = 64 * C
Physical Interpretation
- When the smaller spheres unite, they maintain the same potential but can store more charge due to their increased surface area.
- This results in a larger effective capacitance.
Conclusion
- The formation of a larger spherical conductor from 64 smaller spheres increases the overall capacitance to 64 times the capacitance of an individual sphere.
- This principle illustrates how combining conductors enhances their ability to store electrical energy, which is vital in various applications in electrical engineering and physics.
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How will the capacitance change when 64 spherical conducters of equal size charge potential and capacitance c" each joined together to form a bigger spherical conducter?
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How will the capacitance change when 64 spherical conducters of equal size charge potential and capacitance c" each joined together to form a bigger spherical conducter? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about How will the capacitance change when 64 spherical conducters of equal size charge potential and capacitance c" each joined together to form a bigger spherical conducter? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How will the capacitance change when 64 spherical conducters of equal size charge potential and capacitance c" each joined together to form a bigger spherical conducter?.
How will the capacitance change when 64 spherical conducters of equal size charge potential and capacitance c" each joined together to form a bigger spherical conducter? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about How will the capacitance change when 64 spherical conducters of equal size charge potential and capacitance c" each joined together to form a bigger spherical conducter? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How will the capacitance change when 64 spherical conducters of equal size charge potential and capacitance c" each joined together to form a bigger spherical conducter?.
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