Answer

Verified

52.2k+ views

**Hint**We know the value of conductor length and resistance of any conductive material here, so by using this formula we calculate the end-to-end resistance of a conductor given length and area, we also know that specific resistance is given in units of ohms for materials.

**Useful formula**

Resistance of conductor is given below,

$R = \rho * \left( {\dfrac{L}{A}} \right)$

$R = $ resistance in ohms

$\rho = $ material resistivity in ohms per meter

$L = $ conductor length in meters

$A = $ cross-sectional area in square meters

**Complete step by step procedure**

Given by,

Resistance of a conductor of length $75\,cm$is \[3.25{\text{ }}ohm\]

\[R = 3.25{\text{ }}ohm\] and \[I = 75\,cm\]

Let length of another conductor whose resistance is \[16.25{\text{ }}ohm\]be $x$

\[R{\text{ }} = {\text{ }}16.25{\text{ }}ohm\] \[I = \,x\,cm\]

A conductor's resistance and the conductor's length are directly proportional to one another. The resistance of the conductor also increases as the length of the conductor increases.

The relationship between a conductor's length and resistance is given as $R = \rho * \left( {\dfrac{L}{A}} \right)$

The material of the conductor remains the same, so there is constant resistivity $(\rho )$.

According to that,

The given value in substituting the equation.

So,

$3.25 = \rho \dfrac{{75}}{A}$……………………………. $(1)$

For the resistance to be $13.25$ ohms.

The equation is written as,

$13.25 = \rho \dfrac{x}{A}$……………………………$(2)$

Solving the both equations,

We get,

\[x = 305.76\,cm\]

Hence,

The length of the conductor for it have $13.25\Omega $ resistance is $305.76\,cm$

**Thus, option A is the correct answer.**

**Note**As electrons pass through a conductor, such as a metal wire, an electrical current flow. With the ions in the metal, the moving electrons will collide. It makes it harder for the current to flow. All materials have some resilience, but some materials are more or less resistant to electric current flow than other materials.

Recently Updated Pages

Which is not the correct advantage of parallel combination class 10 physics JEE_Main

State two factors upon which the heat absorbed by a class 10 physics JEE_Main

What will be the halflife of a first order reaction class 12 chemistry JEE_Main

Which of the following amino acids is an essential class 12 chemistry JEE_Main

Which of the following is least basic A B C D class 12 chemistry JEE_Main

Out of the following hybrid orbitals the one which class 12 chemistry JEE_Main

Other Pages

The resultant of vec A and vec B is perpendicular to class 11 physics JEE_Main

If a wire of resistance R is stretched to double of class 12 physics JEE_Main

when an object Is placed at a distance of 60 cm from class 12 physics JEE_Main

Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main

Which of the following sets of displacements might class 11 physics JEE_Main

Explain the construction and working of a GeigerMuller class 12 physics JEE_Main