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Two metal wires of identical dimensions are connected in series. If σ1 and σ2 are the conductivities of the metal wires respectively, the effective conductivity of the combination is
- a)σ1 + σ2
- b)σ1 + σ2 / 2
- c)√σ1σ2
- d)2σ1σ2 / σ1 + σ2
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Two metal wires of identical dimensions are connected in series. If &s...
Resistance of a wire in terms of connectivity (σ) is given by
where l is the length and A is area of cross section of wire respectively.
∴ Rs = R1 + R2
⇒
where σs is the effective conductivity
σs = 2σ1σ2 / σ1 + σ2
where l is the length and A is area of cross section of wire respectively.
∴ Rs = R1 + R2
⇒
where σs is the effective conductivity
σs = 2σ1σ2 / σ1 + σ2
Most Upvoted Answer
Two metal wires of identical dimensions are connected in series. If &s...
- **Effective Conductivity of the Combination**
- **Given:**
- Conductivity of wire 1: σ1
- Conductivity of wire 2: σ2
- **Concept:**
- When two wires are connected in series, the total resistance is the sum of the individual resistances.
- The conductivity (σ) is the reciprocal of resistance (σ = 1/R).
- The effective conductivity of the combination is the reciprocal of the total resistance.
- For two resistors in series, the total resistance (R) is given by the formula:
\[ R = \frac{R1 \times R2}{R1 + R2} \]
where R1 and R2 are the resistances of the individual wires.
- The effective conductivity (σ') is the reciprocal of the total resistance:
\[ \sigma' = \frac{1}{R} = \frac{1}{\frac{1}{\sigma1} + \frac{1}{\sigma2}} \]
- **Calculation:**
- Substituting the values of σ1 and σ2 in the formula, we get:
\[ \sigma' = \frac{1}{\frac{1}{\sigma1} + \frac{1}{\sigma2}} = \frac{2 \times \sigma1 \times \sigma2}{\sigma1 + \sigma2} \]
- **Conclusion:**
- Therefore, the effective conductivity of the combination of two wires connected in series is given by:
\[ \frac{2 \times \sigma1 \times \sigma2}{\sigma1 + \sigma2} \]
- Hence, option 'D' (2σ1σ2 / σ1+σ2) is the correct answer.
- **Given:**
- Conductivity of wire 1: σ1
- Conductivity of wire 2: σ2
- **Concept:**
- When two wires are connected in series, the total resistance is the sum of the individual resistances.
- The conductivity (σ) is the reciprocal of resistance (σ = 1/R).
- The effective conductivity of the combination is the reciprocal of the total resistance.
- For two resistors in series, the total resistance (R) is given by the formula:
\[ R = \frac{R1 \times R2}{R1 + R2} \]
where R1 and R2 are the resistances of the individual wires.
- The effective conductivity (σ') is the reciprocal of the total resistance:
\[ \sigma' = \frac{1}{R} = \frac{1}{\frac{1}{\sigma1} + \frac{1}{\sigma2}} \]
- **Calculation:**
- Substituting the values of σ1 and σ2 in the formula, we get:
\[ \sigma' = \frac{1}{\frac{1}{\sigma1} + \frac{1}{\sigma2}} = \frac{2 \times \sigma1 \times \sigma2}{\sigma1 + \sigma2} \]
- **Conclusion:**
- Therefore, the effective conductivity of the combination of two wires connected in series is given by:
\[ \frac{2 \times \sigma1 \times \sigma2}{\sigma1 + \sigma2} \]
- Hence, option 'D' (2σ1σ2 / σ1+σ2) is the correct answer.
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Two metal wires of identical dimensions are connected in series. If σ1 and σ2 are the conductivities of the metal wires respectively, the effective conductivity of the combination isa)σ1+σ2b)σ1+σ2/ 2c)√σ1σ2d)2σ1σ2/σ1+σ2Correct answer is option 'D'. Can you explain this answer?
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Two metal wires of identical dimensions are connected in series. If σ1 and σ2 are the conductivities of the metal wires respectively, the effective conductivity of the combination isa)σ1+σ2b)σ1+σ2/ 2c)√σ1σ2d)2σ1σ2/σ1+σ2Correct answer is option 'D'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two metal wires of identical dimensions are connected in series. If σ1 and σ2 are the conductivities of the metal wires respectively, the effective conductivity of the combination isa)σ1+σ2b)σ1+σ2/ 2c)√σ1σ2d)2σ1σ2/σ1+σ2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two metal wires of identical dimensions are connected in series. If σ1 and σ2 are the conductivities of the metal wires respectively, the effective conductivity of the combination isa)σ1+σ2b)σ1+σ2/ 2c)√σ1σ2d)2σ1σ2/σ1+σ2Correct answer is option 'D'. Can you explain this answer?.
Two metal wires of identical dimensions are connected in series. If σ1 and σ2 are the conductivities of the metal wires respectively, the effective conductivity of the combination isa)σ1+σ2b)σ1+σ2/ 2c)√σ1σ2d)2σ1σ2/σ1+σ2Correct answer is option 'D'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two metal wires of identical dimensions are connected in series. If σ1 and σ2 are the conductivities of the metal wires respectively, the effective conductivity of the combination isa)σ1+σ2b)σ1+σ2/ 2c)√σ1σ2d)2σ1σ2/σ1+σ2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two metal wires of identical dimensions are connected in series. If σ1 and σ2 are the conductivities of the metal wires respectively, the effective conductivity of the combination isa)σ1+σ2b)σ1+σ2/ 2c)√σ1σ2d)2σ1σ2/σ1+σ2Correct answer is option 'D'. Can you explain this answer?.
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