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A resistance of 2Ω is connected across one gap of a metre-bridge (the length of the wire is 100 cm) and an unknown resistance, greater than 2Ω, is connected across the other gap. When these resistances are interchanged, the balance point shifts by 20 cm. Neglecting any corrections, the unknown resistance is
Correct answer is '3'. Can you explain this answer?
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A resistance of 2Ω is connected across one gap of a metre-bridge (the...
Given, R = 2 Ω
From the first condition,
Now, from the second condition,
Put the value of x from equation (i) in (ii).
⇒ (100 - l)(80 - l) = l(l + 20)
⇒ 8000 - 100l - 80l + l2 = l2 + 20l
⇒ 8000 = 20l + 180l
Put this value in equation (ii).
⇒ x = 3 Ω
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A resistance of 2Ω is connected across one gap of a metre-bridge (the...
Given:
- Resistance across one gap of the metre-bridge = 2Ω
- Length of the wire = 100 cm
Unknown:
- Resistance across the other gap
Additional information:
- When the resistances are interchanged, the balance point shifts by 20 cm.
Approach:
1. Let the unknown resistance be R.
2. Using the concept of a Wheatstone bridge, we can write the equation for the balance point as:
R/2 = (100 - R)/(2 + R)
This equation is derived from the fact that the ratio of resistances on both sides of the bridge is equal.
3. Solve the above equation to find the value of R.
Calculation:
1. Cross-multiply the equation:
R(2 + R) = 2(100 - R)
2R + R^2 = 200 - 2R
R^2 + 4R - 200 = 0
2. Solve the quadratic equation:
Using the quadratic formula, we get:
R = (-4 ± √(4^2 - 4(1)(-200))) / (2(1))
R = (-4 ± √(16 + 800)) / 2
R = (-4 ± √816) / 2
R = (-4 ± 28.57) / 2
R ≈ (-4 + 28.57) / 2 or (-4 - 28.57) / 2
R ≈ 24.57 / 2 or -32.57 / 2
R ≈ 12.285 or -16.285
3. Since the unknown resistance cannot be negative, we discard the negative value.
Therefore, the unknown resistance is approximately 12.285Ω.
Answer:
The unknown resistance is approximately 12.285Ω.
- Resistance across one gap of the metre-bridge = 2Ω
- Length of the wire = 100 cm
Unknown:
- Resistance across the other gap
Additional information:
- When the resistances are interchanged, the balance point shifts by 20 cm.
Approach:
1. Let the unknown resistance be R.
2. Using the concept of a Wheatstone bridge, we can write the equation for the balance point as:
R/2 = (100 - R)/(2 + R)
This equation is derived from the fact that the ratio of resistances on both sides of the bridge is equal.
3. Solve the above equation to find the value of R.
Calculation:
1. Cross-multiply the equation:
R(2 + R) = 2(100 - R)
2R + R^2 = 200 - 2R
R^2 + 4R - 200 = 0
2. Solve the quadratic equation:
Using the quadratic formula, we get:
R = (-4 ± √(4^2 - 4(1)(-200))) / (2(1))
R = (-4 ± √(16 + 800)) / 2
R = (-4 ± √816) / 2
R = (-4 ± 28.57) / 2
R ≈ (-4 + 28.57) / 2 or (-4 - 28.57) / 2
R ≈ 24.57 / 2 or -32.57 / 2
R ≈ 12.285 or -16.285
3. Since the unknown resistance cannot be negative, we discard the negative value.
Therefore, the unknown resistance is approximately 12.285Ω.
Answer:
The unknown resistance is approximately 12.285Ω.
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A resistance of 2Ω is connected across one gap of a metre-bridge (the length of the wire is 100 cm) and an unknown resistance, greater than 2Ω, is connected across the other gap. When these resistances are interchanged, the balance point shifts by 20 cm. Neglecting any corrections, the unknown resistance isCorrect answer is '3'. Can you explain this answer?
Question Description
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A resistance of 2Ω is connected across one gap of a metre-bridge (the length of the wire is 100 cm) and an unknown resistance, greater than 2Ω, is connected across the other gap. When these resistances are interchanged, the balance point shifts by 20 cm. Neglecting any corrections, the unknown resistance isCorrect answer is '3'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A resistance of 2Ω is connected across one gap of a metre-bridge (the length of the wire is 100 cm) and an unknown resistance, greater than 2Ω, is connected across the other gap. When these resistances are interchanged, the balance point shifts by 20 cm. Neglecting any corrections, the unknown resistance isCorrect answer is '3'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A resistance of 2Ω is connected across one gap of a metre-bridge (the length of the wire is 100 cm) and an unknown resistance, greater than 2Ω, is connected across the other gap. When these resistances are interchanged, the balance point shifts by 20 cm. Neglecting any corrections, the unknown resistance isCorrect answer is '3'. Can you explain this answer?.
Solutions for A resistance of 2Ω is connected across one gap of a metre-bridge (the length of the wire is 100 cm) and an unknown resistance, greater than 2Ω, is connected across the other gap. When these resistances are interchanged, the balance point shifts by 20 cm. Neglecting any corrections, the unknown resistance isCorrect answer is '3'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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