In the following question, a Statement of Assertion (A) is given follo...
The effective resistance between any points on the diameter will be 3ohm.. as R is directly proportional to length.. so the wire in the form of circle will be divided into two halves with each half wire having half the resistance of the whole circular wire.. And these two halves will be joined in parallel combination not series.. so the effective resistance as calculated 6×6/6+6 = 3 ohm..
so option (d) is correct as both the assertion and reason are false
In the following question, a Statement of Assertion (A) is given follo...
Assertion: A wire has a resistance of 12Ω. It is bent in the form of a circle. The effective resistance between two points on any diameter is 6Ω.
Reason: Equivalent resistance between two points on any diameter is in series.
To analyze the given assertion and reason, let's break it down into different parts and understand the concepts involved.
Resistance of a wire:
Resistance is a property of a material to oppose the flow of electric current. It is measured in ohms (Ω). The resistance of a wire depends on various factors such as the material used, length, cross-sectional area, and temperature.
Effective resistance:
When resistors are connected in different configurations (series, parallel, or a combination of both), the total resistance offered by the combination is referred to as the effective resistance. It can be calculated using different formulas depending on the configuration.
Wire bent in the form of a circle:
In this scenario, the wire is bent into a circular shape. This means that the wire forms a closed loop, and the current flowing through the wire can circulate around the loop.
Equivalent resistance in series:
When resistors are connected in series, the total resistance is the sum of individual resistances. In other words, the equivalent resistance in a series connection is the algebraic sum of the resistances.
Analysis:
In the given assertion, it is stated that a wire has a resistance of 12Ω and is bent in the form of a circle. The effective resistance between two points on any diameter is mentioned as 6Ω.
The reason provided states that the equivalent resistance between two points on any diameter is in series.
Conclusion:
The given assertion and reason are both false.
Explanation:
- The effective resistance between two points on any diameter of a circular wire does not depend on the resistance of the wire itself. It depends on the length and cross-sectional area of the wire segment between the two points. Therefore, the statement in the assertion that the resistance of the wire is 12Ω is irrelevant to the effective resistance between two points on any diameter.
- The reason provided is incorrect. The equivalent resistance between two points on any diameter is not in series. In fact, the equivalent resistance between two points on any diameter of a circular wire is zero, as there is a direct connection between the two points without any resistance in between.
Therefore, both the assertion and reason are false. The correct answer is option D.
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