Question

Nine identical wires , each of diameter d and length L, are connected in parallel. The combination has the resistance as a single similar wire of length L but whose diameter is ______?

Answer 1

Answer:

Answer is 3d

Explanation:

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Answer 2

The combination has the resistance as a single similar wire of length L but whose diameter is one third of the original diameter.

We know resistance R of a wire is defined as

R = ρ $\frac{l}{A}$

where ρ is resistivity

           l is length of the wire

           A is area of cross section of the conductor

For th given wire R = ρ×$\\\\\frac{l}{3.14(\frac{d}{y2 } )^2}$

Since such nine identical wires  are arranged in parellel combination

$\frac{1}{R_{net} } =\frac{n}{R} \\\frac{1}{R_{net}} =\frac{9}{R}$

Substituting R we get

$R_{net}=\frac{4(rho)(l)}{3.14d^2 } \frac{1}{9}$

Comparing the equation with that of resistance we can say that the combination has a resistance as a aingle similar wire of length L but whose diameter is one third of the original diameter.