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Two rods of the same length and diameter having thermal conductivities K1 and K2 are joined in parallel. The equivalent thermal conductivity of the combination is
- a)K1K2/K1 + K2
- b)K1 + K2
- c)K1 + K2 / 2
- d)√K1K2
Correct answer is option 'C'. Can you explain this answer?
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Two rods of the same length and diameter having thermal conductivities...
2K1K2/ (K1 + K2)
To find the equivalent thermal conductivity of the combination, we can use the formula for thermal resistance in parallel:
1/R = 1/R1 + 1/R2
Where R1 and R2 are the thermal resistances of the two rods, and R is the equivalent thermal resistance of the combination. The thermal resistance is inversely proportional to the thermal conductivity, so we can write:
R1 = L / (K1A)
R2 = L / (K2A)
Where L is the length of the rods and A is the cross-sectional area (assuming the rods have the same cross-sectional area). Substituting these expressions into the formula for parallel resistance, we get:
1/R = K2 / (K1K2 + K2^2) + K1 / (K1K2 + K1^2)
Simplifying this expression, we get:
1/R = (K1 + K2) / (K1K2 + K1^2 + K2^2)
Taking the reciprocal of both sides, we get:
R = (K1K2 + K1^2 + K2^2) / (K1 + K2)
Finally, we can use the formula for thermal conductivity (K = 1/R) to find the equivalent thermal conductivity of the combination:
K = 1/R = (K1 + K2) / (K1K2 + K1^2 + K2^2)
Multiplying the numerator and denominator by 2K1K2, we get:
K = 2K1K2 / (2K1K2 + K1^2 + K2^2)
Therefore, the correct option is d) 2K1K2/ (K1 + K2).
To find the equivalent thermal conductivity of the combination, we can use the formula for thermal resistance in parallel:
1/R = 1/R1 + 1/R2
Where R1 and R2 are the thermal resistances of the two rods, and R is the equivalent thermal resistance of the combination. The thermal resistance is inversely proportional to the thermal conductivity, so we can write:
R1 = L / (K1A)
R2 = L / (K2A)
Where L is the length of the rods and A is the cross-sectional area (assuming the rods have the same cross-sectional area). Substituting these expressions into the formula for parallel resistance, we get:
1/R = K2 / (K1K2 + K2^2) + K1 / (K1K2 + K1^2)
Simplifying this expression, we get:
1/R = (K1 + K2) / (K1K2 + K1^2 + K2^2)
Taking the reciprocal of both sides, we get:
R = (K1K2 + K1^2 + K2^2) / (K1 + K2)
Finally, we can use the formula for thermal conductivity (K = 1/R) to find the equivalent thermal conductivity of the combination:
K = 1/R = (K1 + K2) / (K1K2 + K1^2 + K2^2)
Multiplying the numerator and denominator by 2K1K2, we get:
K = 2K1K2 / (2K1K2 + K1^2 + K2^2)
Therefore, the correct option is d) 2K1K2/ (K1 + K2).
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Two rods of the same length and diameter having thermal conductivities K1 and K2 are joined in parallel. The equivalent thermal conductivity of the combination isa)K1K2/K1+ K2b)K1 + K2c)K1+ K2/ 2d)√K1K2Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two rods of the same length and diameter having thermal conductivities K1 and K2 are joined in parallel. The equivalent thermal conductivity of the combination isa)K1K2/K1+ K2b)K1 + K2c)K1+ K2/ 2d)√K1K2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two rods of the same length and diameter having thermal conductivities K1 and K2 are joined in parallel. The equivalent thermal conductivity of the combination isa)K1K2/K1+ K2b)K1 + K2c)K1+ K2/ 2d)√K1K2Correct answer is option 'C'. Can you explain this answer?.
Two rods of the same length and diameter having thermal conductivities K1 and K2 are joined in parallel. The equivalent thermal conductivity of the combination isa)K1K2/K1+ K2b)K1 + K2c)K1+ K2/ 2d)√K1K2Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two rods of the same length and diameter having thermal conductivities K1 and K2 are joined in parallel. The equivalent thermal conductivity of the combination isa)K1K2/K1+ K2b)K1 + K2c)K1+ K2/ 2d)√K1K2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two rods of the same length and diameter having thermal conductivities K1 and K2 are joined in parallel. The equivalent thermal conductivity of the combination isa)K1K2/K1+ K2b)K1 + K2c)K1+ K2/ 2d)√K1K2Correct answer is option 'C'. Can you explain this answer?.
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