Two metallic wires made from copper have same length but the radius of wire 1 is half of that of wire 2. The resistance of wire 1 is R. If both the wires are joined together in series, the total resistance becomes

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Q: 33 (CDS-I/2018)
Two metallic wires made from copper have same length but the radius of wire 1 is half of that of wire
2. The resistance of wire 1 is R. If both the wires are joined together in series, the total resistance becomes

question_subject: 

Science

question_exam: 

CDS-I

stats: 

0,5,10,6,2,5,2

keywords: 

{'metallic wires': [0, 0, 0, 1], 'total resistance': [0, 0, 0, 3], 'resistance': [0, 0, 1, 2], 'wires': [0, 0, 1, 1], 'copper': [1, 0, 1, 1], 'wire': [0, 0, 7, 16], 'same length': [0, 1, 0, 2], 'radius': [0, 0, 2, 2], 'series': [0, 1, 1, 0], 'half': [5, 2, 5, 2]}

When two metallic wires made from copper are joined together in series, their total resistance is equal to the sum of their individual resistances.

In this scenario, wire 1 has a radius that is half of wire 2. We know that resistance is inversely proportional to the cross-sectional area of a wire. Since the radius affects the cross-sectional area, we can conclude that the resistance of wire 2 is four times that of wire 1 (because the radius is twice as large).

Now, if we join these two wires in series, the total resistance will be equal to the sum of their resistances. That means, the total resistance will be 4R + R = 5R.

Therefore, the correct answer is option 3 – 5R. The total resistance when the wires are joined in series is five times the resistance of wire 1 alone.