Question

The resistance of a wire is R. It is bent at the middle by ${180^ \circ }$ and both the ends are twisted together to make a shorter wire. The resistance of the new wire is ?
A) 2R
B) R/2
C) R/4
D) R/8

Answer 1

Hint:The question is from the electricity part of physics. This problem is solved by using resistivity concepts. We can use the equation resistance of a wire directly to this question.

Formula Used:
The relation between resistance and length of material (wire) is
$R = \dfrac{{\rho L}}{A}$
Where,
$R$ = Resistance of the material
$\rho $ = resistivity of the material
$L$ = length of the material
$A$ = cross-sectional area of the material


Complete answer:
The relation between resistance and length of wire is
$R = \dfrac{{\rho L}}{A}$
Where,
$R$ = Resistance of the wire
$\rho $ = resistivity of the wire
$L$ = length of the wire
$A$ = cross-sectional area of the wire
In this case, The wire is bent in the middle and rotates ${180^ \circ }$. When both the ends of the wire are twisted together to make it shorter. Now the new length of the wire is,
${L_1} = \dfrac{L}{2}$
After the changes, the cross-sectional area of the wire is given below.
${A_1} = 2A$
Substitute these values in the resistivity equation.
\[{R_1} = \dfrac{{\rho {L_1}}}{{{A_1}}}\]
\[{R_1} = \dfrac{\rho }{{2A}}\dfrac{L}{2}\]
\[\begin{array}{l}{R_1} = \dfrac{{\rho L}}{{4A}}\\\end{array}\]
\[{R_1} = \dfrac{R}{4}\]

Hence, the correct option is Option C) R/4.

Additional Information: Resistance is a measure of the opposition to current flow in an electrical circuit. The relation between length and resistance of the material is given by the resistivity formula. Resistance is directly proportional to the length. That means any change in the length of the material will change its value of resistance. The electric resistance is measured in ohm ($\Omega $).
1 $\Omega $ = 1 V/A.

Note: Resistance counteracts the current flow. The greater the resistance of the material, the lower the flow of current. Similarly, the lower the resistance, the greater the flow of current.