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A wire of resistance. 1 ohm per centimetre bent to form a square ABCD of side 10cm . A similar wire is connected between the corners B and D to form diagonal BD find the effective resistance of combination between the corners A and C?
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A wire of resistance. 1 ohm per centimetre bent to form a square ABCD ...
Analysis:
The given wire has a resistance of 1 ohm per centimetre. The wire is bent to form a square ABCD with each side measuring 10 cm. Another wire is connected between the corners B and D to form the diagonal BD.
Calculating the resistance of the diagonal BD:
- The length of the diagonal BD can be calculated using Pythagoras theorem as it forms the hypotenuse of a right-angled triangle with sides 10 cm each.
- Using the formula, length of diagonal = √(side^2 + side^2) = √(10^2 + 10^2) = √200 cm
- The resistance of the diagonal BD can be calculated by multiplying the length of the diagonal by the resistance per centimetre.
- Resistance of BD = √200 * 1 ohm = √200 ohm
Calculating the effective resistance between A and C:
- The square ABCD can be divided into two triangles by the diagonal BD.
- The resistance between A and C can be calculated as the sum of resistances in the path AC and the path BD.
- Resistance between A and C = Resistance of AC + Resistance of BD
- Resistance of AC can be calculated as the sum of the resistances of sides AB, BC, and CD.
- Resistance of AC = 10*1 + 10*1 + 10*1 = 30 ohm
- Therefore, the effective resistance between A and C is 30 ohm + √200 ohm = 30 + √200 ohm.
In conclusion, the effective resistance between the corners A and C of the square formed by the wire is 30 + √200 ohm.
The given wire has a resistance of 1 ohm per centimetre. The wire is bent to form a square ABCD with each side measuring 10 cm. Another wire is connected between the corners B and D to form the diagonal BD.
Calculating the resistance of the diagonal BD:
- The length of the diagonal BD can be calculated using Pythagoras theorem as it forms the hypotenuse of a right-angled triangle with sides 10 cm each.
- Using the formula, length of diagonal = √(side^2 + side^2) = √(10^2 + 10^2) = √200 cm
- The resistance of the diagonal BD can be calculated by multiplying the length of the diagonal by the resistance per centimetre.
- Resistance of BD = √200 * 1 ohm = √200 ohm
Calculating the effective resistance between A and C:
- The square ABCD can be divided into two triangles by the diagonal BD.
- The resistance between A and C can be calculated as the sum of resistances in the path AC and the path BD.
- Resistance between A and C = Resistance of AC + Resistance of BD
- Resistance of AC can be calculated as the sum of the resistances of sides AB, BC, and CD.
- Resistance of AC = 10*1 + 10*1 + 10*1 = 30 ohm
- Therefore, the effective resistance between A and C is 30 ohm + √200 ohm = 30 + √200 ohm.
In conclusion, the effective resistance between the corners A and C of the square formed by the wire is 30 + √200 ohm.
Community Answer
A wire of resistance. 1 ohm per centimetre bent to form a square ABCD ...
10 ohm is this correct
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A wire of resistance. 1 ohm per centimetre bent to form a square ABCD of side 10cm . A similar wire is connected between the corners B and D to form diagonal BD find the effective resistance of combination between the corners A and C?
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A wire of resistance. 1 ohm per centimetre bent to form a square ABCD of side 10cm . A similar wire is connected between the corners B and D to form diagonal BD find the effective resistance of combination between the corners A and C? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A wire of resistance. 1 ohm per centimetre bent to form a square ABCD of side 10cm . A similar wire is connected between the corners B and D to form diagonal BD find the effective resistance of combination between the corners A and C? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wire of resistance. 1 ohm per centimetre bent to form a square ABCD of side 10cm . A similar wire is connected between the corners B and D to form diagonal BD find the effective resistance of combination between the corners A and C?.
A wire of resistance. 1 ohm per centimetre bent to form a square ABCD of side 10cm . A similar wire is connected between the corners B and D to form diagonal BD find the effective resistance of combination between the corners A and C? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A wire of resistance. 1 ohm per centimetre bent to form a square ABCD of side 10cm . A similar wire is connected between the corners B and D to form diagonal BD find the effective resistance of combination between the corners A and C? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wire of resistance. 1 ohm per centimetre bent to form a square ABCD of side 10cm . A similar wire is connected between the corners B and D to form diagonal BD find the effective resistance of combination between the corners A and C?.
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