Question

When a potential difference of 10V is placed across a certain solid cylindrical resistor with resistivity p, the current through it is 2A. If the diameter of this resistor is now tripled, the current will be?

Answer 1

Concepts and reason

The concepts used in this problem are Ohm’s law and the relation between resistivity and resistance.

At first, use Ohm’s law and formula of resistivity to get the relation of the current in terms of potential difference, resistivity, and diameter of the wire.

Later, use the given conditions provided in the question to get the required value of the current.

Fundamentals

Resistance and Resistivity:

The relation between resistance and resistivity is:

$R = \frac{{\rho L}}{A}$

Here, $\rho$ is the resistivity, $R$ is the resistance, $L$ is the length and $A$ is the cross-sectional area.

Ohm’s Law:

According to Ohm’s Law, “the voltage is directly proportional to the current”

Here, $V$ is the voltage, $I$ is current and $R$ is the resistance.

According to Ohm’s law,

…… (1)

The resistance is,

…… (2)

Substitute equation (2) in equation (1).

…… (3)

The surface area of the resistor is,

…… (4)

Here, is the diameter of the resistor.

Substitute equation (4) in equation (3).

The expression of the current is,

Except for the diameter, all other parameters are constant. So, the current is directly proportional to the square of the diameter.

Here, and are the diameters and is the new current.

The new current is,

Substitute for and for in the above equation.

Ans:

The current through the resistor is.