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Five equally sized sections are cut from a wire of resistance $R_{1}$ . Then, a parallel connection is made using these five sections of the wire. If the total resistance of this combination is $R_{2},$ then $\frac{R_{1}}{R_{2}}$ is [[1]].

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Detailed Solution

Let the resistance of each section of the wire is R, the total resistance of the wire when the sections are connected in series is:

R_{1} = R + R + R + R + R

(The sections can be assumed in series when it is a complete wire )

R_{1} = 5 R

And, the total resistance of the combination when the sections are connected in parallel is:

R_{2} = \frac{R}{5}

Hence,

\frac{R_{1}}{R_{2}} = \frac{5 R}{R / 5}

\frac{R_{1}}{R_{2}} = 25

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