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When diameter of the core and cable is doubled the value of capacitance
- a)will be reduced to one fourth
- b)will be reduced to half
- c)will be doubled
- d)will become four times
Correct answer is option 'A'. Can you explain this answer?
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When diameter of the core and cable is doubled the value of capacitanc...
Explanation:
Capacitance is defined as the ability of a system to store an electric charge. It depends on the geometric properties of the system, such as the distance between the two conductors and the area of the conductors.
When the diameter of the core and cable is doubled, the following changes occur:
1. Distance between the conductors: The distance between the two conductors is increased by a factor of 2. This is because the diameter of the core and cable has been doubled, and the conductors are located at the center of the core and cable.
2. Area of the conductors: The area of the conductors is increased by a factor of 4. This is because the area of a circle is proportional to the square of its diameter.
As a result of the above changes, the capacitance of the system is reduced to one-fourth of its original value. This is because capacitance is inversely proportional to the distance between the conductors and directly proportional to the area of the conductors.
Mathematically, the capacitance of a system is given by the formula:
C = εA/d
where C is the capacitance, ε is the permittivity of the medium between the conductors, A is the area of the conductors, and d is the distance between the conductors.
When the diameter of the core and cable is doubled, the value of A is increased by a factor of 4, and the value of d is increased by a factor of 2. Therefore, the capacitance is reduced by a factor of (1/4) x (1/2) = 1/8 or one-fourth.
Capacitance is defined as the ability of a system to store an electric charge. It depends on the geometric properties of the system, such as the distance between the two conductors and the area of the conductors.
When the diameter of the core and cable is doubled, the following changes occur:
1. Distance between the conductors: The distance between the two conductors is increased by a factor of 2. This is because the diameter of the core and cable has been doubled, and the conductors are located at the center of the core and cable.
2. Area of the conductors: The area of the conductors is increased by a factor of 4. This is because the area of a circle is proportional to the square of its diameter.
As a result of the above changes, the capacitance of the system is reduced to one-fourth of its original value. This is because capacitance is inversely proportional to the distance between the conductors and directly proportional to the area of the conductors.
Mathematically, the capacitance of a system is given by the formula:
C = εA/d
where C is the capacitance, ε is the permittivity of the medium between the conductors, A is the area of the conductors, and d is the distance between the conductors.
When the diameter of the core and cable is doubled, the value of A is increased by a factor of 4, and the value of d is increased by a factor of 2. Therefore, the capacitance is reduced by a factor of (1/4) x (1/2) = 1/8 or one-fourth.
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