Question

Resistance of a conductor of length $75cm$ is $3.25\Omega$. What will be the length of a similar conductor whose resistance is $13.25\Omega$ ?

• A. $305.76cm$
• B. $503.76cm$
• C. $200cm$
• D. $610cm$

Answer 1

The correct option is A $305.76cm$

The resistance of a conductor and length of the conductor are directly proportional to each other. As the length of the conductor increases, the resistance of the conductor also increases. The relation between the length and resistance of a conductor is given as $R=\rho \frac{l}{A}$.
In this case, Resistance of a conductor of length 75 cm is 3.25 ohms. The material of the conductor remains the same so resistivity ($\rho$) is constant.
So, $3.25=\rho \frac{75}{A}$. _____ Eqn 1
For the resistance to be 13.25 ohms, the equation is written as
$13.25=\rho \frac{x}{A}$ _____ Eqn 2
Solving both equations we get x=305.76 cm.
Hence, the length of the conductor for it have $13.25\Omega$ resistance is $305.76cm.$