Question

you are given a 8 ohm resistorwhat length of constantan wire of resistance 120 ohm/m should be joined in parallel with it to get a value of 6 ohm

Answer 1

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Answer 2

Concept Introduction:

Resistors connected in parallel are related as: $Req=\frac{R1*R2}{R1+R2}$

Given: $8$ ohm resistor joined to another resistor to give equivalent resistance of $6$ ohm.

To Find:

We have to find the value of, length of constantan wire of resistance $120 ohm/m$.

Solution:

According to the problem,

The resistor that is to joined to $8ohm$ resistor to obtain resistor of $6ohm$ is:

$6=\frac{8*R}{8+R}$

⇒$48+6R=8R$

⇒$2R=48$

⇒$R=24$$ohm$

∴ Length of wire is:

$120ohm$ in $1m$

⇒$24ohm$ in $\frac{1*24}{120} =0.2m$

Final Answer:

The value of length of wire should be $0.2m$.

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