Question

Resistance and Resistivity: The length of a certain wire is doubled while its radius is kept constant. What is the new resistance of this wire?

Answers

  1. Answer:

    Explanation:

    The formula for calculating the resistance of a material in terms of its resistivity is expressed as R = \rho L/A where;

    R is the resistance of the material

    \rho is the resistivity of the material

    L is the length of the wire

    A is the area = πr² with r being the radius

    R = \rho L/\pi r^{2}

    If the length of a certain wire is doubled while its radius is kept constant, then the new length of the wire L₁ = 2L

    The new resistance of the wire R₁ will be expressed as R_1 = \frac{\rho L_1}{A_1}

    since the radius is constant, the area will also be the same i.e A = A₁ and the resistivity also will be constant. The new resistance will become

    R_1 = \frac{\rho(2L)}{A}

    R_1 = \frac{2\rho L}{\pi r^2}

    Taking the ratio of both resistances, we will have;

    \frac{R_1}{R} = \frac{2\rho L/\pi r^2}{\rho L/ \pi r^2} \\\\\frac{R_1}{R} = \frac{2\rho L}{\pi r^2} * \frac{\pi r^2}{ \rho L} \\\\\frac{R_1}{R} = \frac{2}{1}\\\\R_1 = 2R

    This shoes that the new resistance of the wire will be twice that of the original wire

Leave a Comment