Two resistors RY and R2 arranged in parallel combination in an electrical closed circuit are made of the same material and of same thickness. If the length of R2 is twice the length of Rlt then the total resistance R satisfies

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Q: 47 (NDA-I/2022)
Two resistors RY and R2 arranged in parallel combination in an electrical closed circuit are made of the same material and of same thickness. If the length of R2 is twice the length of Rlt then the total resistance R satisfies

question_subject: 

Science

question_exam: 

NDA-I

stats: 

0,10,14,10,4,7,3

keywords: 

{'resistors ry': [0, 0, 0, 1], 'r2': [0, 0, 1, 3], 'parallel combination': [0, 0, 0, 3], 'rlt': [0, 0, 0, 1], 'r1': [0, 0, 0, 2], 'electrical closed circuit': [0, 0, 0, 1], 'same thickness': [0, 0, 0, 1], 'length': [0, 0, 1, 0]}

The correct answer is option 1: 3R = 2RX.

In a parallel combination, the total resistance is given by the formula:

1/R = 1/R1 + 1/R2 .....(1)

Given that R1 and R2 are made of the same material and of the same thickness, we can assume that the resistances are directly proportional to their lengths.

Let the length of R1 be L and the length of R2 be 2L.

Substituting these values into equation (1), we get:

1/R = 1/R1 + 1/R2

1/R = 1/L + 1/(2L)

1/R = (2 + 1)/(2L)

1/R = 3/(2L)

To eliminate the fraction, we can multiply both sides of the equation by 2L:

2L/R = 3

2R = 3(2L)

3R = 2(2L)

3R = 4L

Since R is proportional to L, we can write this equation as:

3R = 2RX

Hence, the correct answer is option 1: 3R = 2RX.