An electric wire of resistance 50 ohm is cut into five equal wires. These wires are then connected in parallel. What is the equivalent resistance of this combination?

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Q: 5 (NDA-I/2022)
An electric wire of resistance 50 ohm is cut into five equal wires. These wires are then connected in parallel. What is the equivalent resistance of this combination?

question_subject: 

Science

question_exam: 

NDA-I

stats: 

0,28,49,28,19,17,13

keywords: 

{'equivalent resistance': [0, 0, 0, 3], 'equal wires': [0, 0, 0, 1], 'resistance': [0, 0, 1, 2], 'electric wire': [0, 0, 0, 1], 'parallel': [0, 1, 3, 5], 'wires': [0, 0, 1, 1], 'combination': [1, 0, 1, 4]}

In this question, an electric wire of resistance 50 ohm is cut into five equal wires. These wires are then connected in parallel. To find the equivalent resistance of this combination, we need to understand how resistances combine in parallel.

When resistances are connected in parallel, the total resistance is inversely proportional to the sum of the reciprocals of each individual resistance.

In this case, since the five equal wires are connected in parallel, the resistance of each individual wire will be the same. So, the equivalent resistance can be calculated as:

1/Req = 1/R1 + 1/R2 + 1/R3 + 1/R4 + 1/R5

Since all the resistors have the same resistance, we can rewrite the equation as:

1/Req = 1/R + 1/R + 1/R + 1/R + 1/R = 5/R

To find Req, we can rearrange the equation:

Req = R/5

Since the given resistance of each wire is 50 ohm, the equivalent resistance of the combination will be:

Req = 50 ohm / 5 = 10 ohm

Therefore, the correct answer is option 2, 10 ohm.