Question

A length of wire is cut in half and the two lengths are wrapped together side by side to make a thicker wire. Part A How does the resistance of this new combination compare to the resistance of the original wire?

Answer 1

Answer:

The resistance of the new combination is one-fourth of the resistance of the original wire.

Explanation:

Let the original length of wire be 'L' and original area of cross section be 'A'.

Now, we know that resistance of old wire is given as:

$R_{old}=\frac{\rho L}{A}$

Where, $\rho\to specific\ resistivity$

Given:

A length of wire is cut in half and the ends are joined to make a thicker wire.

So, new length of wire is half of original length and new area is double of the original area.

So, $L_{new}=\frac{L}{2}$

$A_{new}=2A$

The value of specific resistivity depends on the material used. Since, the wire is same, the value of $\rho$ remains constant.

Therefore, the new resistance is given as:

$R_{new}=\frac{\rho L_{new}}{A_{new}}\\\\R_{new}=\frac{\rho \frac{L}{2}}{2A}\\\\R_{new}=\frac{\rho L}{4A}\\\\R_{new}=\frac{1}{4}(\frac{\rho L}{A})\\\\But,\ \frac{\rho L}{A}=R_{old}\\\\\therefore R_{new}=\frac{1}{4}R_{old}$

Therefore, the resistance of the new combination is one-fourth of the resistance of the original wire.

Answer 2

The resistance of the new combination is four times less than that of the original.

Resistance:

The resistance of a wire is given by:

$R=\rho\frac{L}{A}$

where ρ is the resistivity of the material of the wire

L is the length of the wire, and

A is the cross-sectional area of the wire.

Now, the wire is cut in half and the two halves are joined side by side. So the new length is L/2 and the cross-sectional area now becomes 2A.

So the resistance becomes:

$R'=\rho\frac{L/2}{2A}\\\\R'=\rho\frac{L}{4A}\\\\R'=\frac{1}{4}R$

So the resistance decreases by four times.

Learn more about resistivity and resistance:

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