Question

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

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

Answer 1

Answer: (A)

Answer is A.

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 has 13.25 ohms resistance is 305.76 cm.