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Consider a rectangular slab of length L and cross section area A. A current I is passed through it . If the length is doubled, the potential drop across the end faces (a)becomes half of the initial value (b)becomes 1/4 of the initial value (c)becomes double the initial value (d) remains same Correct option is (c) , can you explain it in detail ?
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Consider a rectangular slab of length L and cross section area A. A cu...
Explanation:
When a current I is passed through the rectangular slab of length L and cross-sectional area A, a potential difference V is developed across the ends of the slab. This potential difference is given by Ohm's law as:
V = IR
where R is the resistance of the slab.
Case 1: When the length of the slab is doubled, i.e., L → 2L
The resistance of the slab is given by:
R = ρL/A
where ρ is the resistivity of the material.
So, when L is doubled, the resistance becomes:
R' = ρ(2L)/A = 2ρL/A = 2R
Therefore, the potential difference across the ends of the slab becomes:
V' = IR' = I(2R) = 2IR
Thus, the potential difference doubles when the length is doubled.
Case 2: When the potential drop across the end faces becomes half of the initial value.
Let the initial potential difference be V and the final length of the slab be 2L. Then, we have:
V' = V/2
Using Ohm's law, we have:
V = IR
V' = I(2R)
Therefore, we have:
V/2 = I(2R)
or, V = 4IR
Now, using the formula for resistance of the slab, we have:
R = ρL/A
and
R' = ρ(2L)/A = 2ρL/A = 2R
Therefore, we have:
V' = I(2R') = I(4R) = 4IR
which is not equal to V/2. Hence, option (a) is incorrect.
Case 3: When the potential drop across the end faces becomes 1/4 of the initial value.
Let the initial potential difference be V and the final length of the slab be 2L. Then, we have:
V' = V/4
Using Ohm's law, we have:
V = IR
V' = I(2R)
Therefore, we have:
V/4 = I(2R)
or, V = 8IR
Now, using the formula for resistance of the slab, we have:
R = ρL/A
and
R' = ρ(2L)/A = 2ρL/A = 2R
Therefore, we have:
V' = I(2R') = I(4R) = 2IR
which is not equal to V/4. Hence, option (b) is incorrect.
Conclusion: Therefore, the correct option is (c) i.e., the potential difference across the ends of the slab becomes double the initial value when the length is doubled.
When a current I is passed through the rectangular slab of length L and cross-sectional area A, a potential difference V is developed across the ends of the slab. This potential difference is given by Ohm's law as:
V = IR
where R is the resistance of the slab.
Case 1: When the length of the slab is doubled, i.e., L → 2L
The resistance of the slab is given by:
R = ρL/A
where ρ is the resistivity of the material.
So, when L is doubled, the resistance becomes:
R' = ρ(2L)/A = 2ρL/A = 2R
Therefore, the potential difference across the ends of the slab becomes:
V' = IR' = I(2R) = 2IR
Thus, the potential difference doubles when the length is doubled.
Case 2: When the potential drop across the end faces becomes half of the initial value.
Let the initial potential difference be V and the final length of the slab be 2L. Then, we have:
V' = V/2
Using Ohm's law, we have:
V = IR
V' = I(2R)
Therefore, we have:
V/2 = I(2R)
or, V = 4IR
Now, using the formula for resistance of the slab, we have:
R = ρL/A
and
R' = ρ(2L)/A = 2ρL/A = 2R
Therefore, we have:
V' = I(2R') = I(4R) = 4IR
which is not equal to V/2. Hence, option (a) is incorrect.
Case 3: When the potential drop across the end faces becomes 1/4 of the initial value.
Let the initial potential difference be V and the final length of the slab be 2L. Then, we have:
V' = V/4
Using Ohm's law, we have:
V = IR
V' = I(2R)
Therefore, we have:
V/4 = I(2R)
or, V = 8IR
Now, using the formula for resistance of the slab, we have:
R = ρL/A
and
R' = ρ(2L)/A = 2ρL/A = 2R
Therefore, we have:
V' = I(2R') = I(4R) = 2IR
which is not equal to V/4. Hence, option (b) is incorrect.
Conclusion: Therefore, the correct option is (c) i.e., the potential difference across the ends of the slab becomes double the initial value when the length is doubled.
Community Answer
Consider a rectangular slab of length L and cross section area A. A cu...
V proportional to R R=¶ L/A
R proportional to L
other things are
R proportional to L
other things are
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Consider a rectangular slab of length L and cross section area A. A current I is passed through it . If the length is doubled, the potential drop across the end faces (a)becomes half of the initial value (b)becomes 1/4 of the initial value (c)becomes double the initial value (d) remains same Correct option is (c) , can you explain it in detail ?
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Consider a rectangular slab of length L and cross section area A. A current I is passed through it . If the length is doubled, the potential drop across the end faces (a)becomes half of the initial value (b)becomes 1/4 of the initial value (c)becomes double the initial value (d) remains same Correct option is (c) , can you explain it in detail ? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Consider a rectangular slab of length L and cross section area A. A current I is passed through it . If the length is doubled, the potential drop across the end faces (a)becomes half of the initial value (b)becomes 1/4 of the initial value (c)becomes double the initial value (d) remains same Correct option is (c) , can you explain it in detail ? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a rectangular slab of length L and cross section area A. A current I is passed through it . If the length is doubled, the potential drop across the end faces (a)becomes half of the initial value (b)becomes 1/4 of the initial value (c)becomes double the initial value (d) remains same Correct option is (c) , can you explain it in detail ?.
Consider a rectangular slab of length L and cross section area A. A current I is passed through it . If the length is doubled, the potential drop across the end faces (a)becomes half of the initial value (b)becomes 1/4 of the initial value (c)becomes double the initial value (d) remains same Correct option is (c) , can you explain it in detail ? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Consider a rectangular slab of length L and cross section area A. A current I is passed through it . If the length is doubled, the potential drop across the end faces (a)becomes half of the initial value (b)becomes 1/4 of the initial value (c)becomes double the initial value (d) remains same Correct option is (c) , can you explain it in detail ? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a rectangular slab of length L and cross section area A. A current I is passed through it . If the length is doubled, the potential drop across the end faces (a)becomes half of the initial value (b)becomes 1/4 of the initial value (c)becomes double the initial value (d) remains same Correct option is (c) , can you explain it in detail ?.
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Consider a rectangular slab of length L and cross section area A. A current I is passed through it . If the length is doubled, the potential drop across the end faces (a)becomes half of the initial value (b)becomes 1/4 of the initial value (c)becomes double the initial value (d) remains same Correct option is (c) , can you explain it in detail ?, a detailed solution for Consider a rectangular slab of length L and cross section area A. A current I is passed through it . If the length is doubled, the potential drop across the end faces (a)becomes half of the initial value (b)becomes 1/4 of the initial value (c)becomes double the initial value (d) remains same Correct option is (c) , can you explain it in detail ? has been provided alongside types of Consider a rectangular slab of length L and cross section area A. A current I is passed through it . If the length is doubled, the potential drop across the end faces (a)becomes half of the initial value (b)becomes 1/4 of the initial value (c)becomes double the initial value (d) remains same Correct option is (c) , can you explain it in detail ? theory, EduRev gives you an
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