A copper wire of radius r and length I has a resistance of R. A second copper wire with radius 2r and length I is taken and the two wires are joined in a parallel combination. The resultant resistance of the parallel combination of the two wires will be

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Q: 28 (CDS-I/2017)
A copper wire of radius r and length I has a resistance of R. A second copper wire with radius 2r and length I is taken and the two wires are joined in a parallel combination. The resultant resistance of the parallel combination of the two wires will be

question_subject: 

Science

question_exam: 

CDS-I

stats: 

0,1,12,4,4,4,1

keywords: 

{'resultant resistance': [0, 0, 0, 2], 'second copper wire': [0, 0, 0, 1], 'copper wire': [0, 0, 0, 3], 'resistance': [0, 0, 1, 2], 'parallel combination': [0, 0, 0, 3], 'wires': [0, 0, 1, 1], 'radius 2r': [0, 0, 0, 1], 'length': [0, 0, 1, 0]}

When two resistors are connected in parallel, their total resistance is given by the formula:

1/R_total = 1/R_1 + 1/R_2

Let`s analyze the given scenario:

Option 1: The radius of the second wire is double the radius of the first wire. However, since the resistances are not directly proportional to the radius, this option is not correct.

Option 2: The resistance of the second wire is double the resistance of the first wire. However, since the resistances decrease when two resistors are in parallel, this option is not correct.

Option 3: The resistance of the second wire is four times the resistance of the first wire. However, as mentioned earlier, the resistances decrease when two resistors are in parallel, so this option is not correct.

Option 4: The resistance of the second wire is half the resistance of the first wire. When two resistors with the same resistance are connected in parallel, the resultant resistance is halved. Therefore, this option is correct.

In conclusion, the correct answer is option 4.