Question

What will be the length of a nichrome wire resistance 5.0Ω, if the length of similar wire of 120 cm has resistance of 2.5 Ω? Why?

Answer 1

$\huge\star{\green{\underline{\mathfrak{Answer :-}}}}$

Given:

Resistance of nichrome wire = 5 Ω

The length of the similar wire with Resistance 2.5 Ω = 120 cm

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To Find:

Length of the wire which has resistance 5 Ω

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Solution:

We know that,

$\tt{\red{R=\rho\dfrac{l}{A}}}$

Now, situation 1,

$\tt{R_1=\rho\dfrac{l_1}{A_1}}$

$\leadsto\tt{5=\rho\dfrac{l_1}{A_1}}$...(1)

Now, situation 2,

$\tt{R_2=\rho\dfrac{l_2}{A_2}}$

$\leadsto\tt{2.5=\rho\dfrac{120}{A_1}}$...(2)

Now, we know, $\tt{A=A_1=A_2}$

(this is because both of them are same wire).....(3)

Finding length of the wire with resistance 5 Ω,

$\leadsto\tt{\dfrac{5=\cancel{\rho}\dfrac{l_1}{A_1}}{2.5=\cancel{\rho}\dfrac{120}{A_2}}}$

Now, from (3),

$\leadsto\tt{\dfrac{5=\cancel{\rho}\dfrac{l_1}{\cancel{A_1}}}{2.5=\cancel{\rho}\dfrac{120}{\cancel{A_2}}}}$

$\leadsto\tt{\dfrac{5}{2.5}=\dfrac{l_1}{120}}$

$\leadsto\tt{5\times 120=l_1 \times 2.5}$

$\leadsto\tt{l_1=\dfrac{5\times 120}{2.5}}$

$\leadsto{\red{\tt{l_1=240\:m}}}$

So, Answer: 240 m.

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