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A copper wire of resistance R is cut into ten parts of equal length. Two pieces each are joined in series and then five such combinations are joined in parallel. The new combination will have a resistance
- a)R
- b)R/4
- c)R/5
- d)R/25
Correct answer is option 'D'. Can you explain this answer?
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A copper wire of resistance R is cut into ten parts of equal length. T...
Solution:
Given, a copper wire of resistance R is cut into ten parts of equal length.
Let each part of the wire have resistance r = R/10.
Two pieces each are joined in series.
The resistance of two pieces joined in series is the sum of their resistances.
Therefore, the resistance of two pieces joined in series is 2r.
Five such combinations are joined in parallel.
When resistors are joined in parallel, the reciprocal of their individual resistances is added and the sum is taken. Then, the reciprocal of the sum is taken to get the equivalent resistance.
Therefore, the equivalent resistance of five combinations joined in parallel is:
1/[(2r)+(2r)] + 1/[(2r)+(2r)] + 1/[(2r)+(2r)] + 1/[(2r)+(2r)] + 1/[(2r)+(2r)]
= 5/[(2r)+(2r)]
= 5/(4r)
= 5/(4(R/10))
= 5/[(4/10)R]
= 5/(2*2*5*R/100)
= 100/(2*2*5*R)
= R/25
Hence, the new combination will have a resistance of R/25.
Therefore, option (d) is the correct answer.
Given, a copper wire of resistance R is cut into ten parts of equal length.
Let each part of the wire have resistance r = R/10.
Two pieces each are joined in series.
The resistance of two pieces joined in series is the sum of their resistances.
Therefore, the resistance of two pieces joined in series is 2r.
Five such combinations are joined in parallel.
When resistors are joined in parallel, the reciprocal of their individual resistances is added and the sum is taken. Then, the reciprocal of the sum is taken to get the equivalent resistance.
Therefore, the equivalent resistance of five combinations joined in parallel is:
1/[(2r)+(2r)] + 1/[(2r)+(2r)] + 1/[(2r)+(2r)] + 1/[(2r)+(2r)] + 1/[(2r)+(2r)]
= 5/[(2r)+(2r)]
= 5/(4r)
= 5/(4(R/10))
= 5/[(4/10)R]
= 5/(2*2*5*R/100)
= 100/(2*2*5*R)
= R/25
Hence, the new combination will have a resistance of R/25.
Therefore, option (d) is the correct answer.
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A copper wire of resistance R is cut into ten parts of equal length. T...
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A copper wire of resistance R is cut into ten parts of equal length. Two pieces each are joined in series and then five such combinations are joined in parallel. The new combination will have a resistancea)Rb)R/4c)R/5d)R/25Correct answer is option 'D'. Can you explain this answer?
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