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CBSE Class 10 Science Question 26 of 45

Solved 2024 Sample Question Paper CBSE Class 10 Science — Question 6

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Question

Question 25(a)

A piece of wire of resistance R is cut into three equal parts. These parts are then connected in parallel. If the equivalent resistance of this parallel combination is R1, what is the value of the ratio R1 : R?

Answer

Given,

Wire of resistance R is cut into three parts so resistance of each part = R3\dfrac{\text{R}}{3} Ω. [∵ resistance is proportional to the length of the wire]

3 wires of resistance R3\dfrac{\text{R}}{3} Ω are connected in parallel and its equivalent resistance = R1 Ω

So, 1R1\dfrac{1}{\text{R}_1} = 3R\dfrac{3}{\text{R}} + 3R\dfrac{3}{\text{R}} + 3R\dfrac{3}{\text{R}} = 9R\dfrac{9}{\text{R}} Ω

Hence, R1 = R9\dfrac{\text{R}}{9}

Ratio of R1 : R = ?

R1R=R9R=R9×R=19\dfrac{\text{R}_1}{\text{R}} = \dfrac{\dfrac{\text{R}}{9}}{\text{R}} \\[1em] = \dfrac{\text{R}}{9 \times R} \\[1em] = \dfrac{1}{9}

∴ Ratio R1 : R = 19\dfrac{1}{9}