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?

The new current will be 18 ampere

Explanation:

1- getting the initial resistance of the wire:

Based on Ohm's law:

We are given that:

At V=10 volts, the current is 2A

This means that:

10 = 2*R

R₁ = 5 ohm

2- getting the final resistance of the wire:

Resistance, resistivity and area of a wire are connected by the following rule:

We also know that the area of the cylinder is πr²

Therefore:

This means that at constant resistivity and length, the resistance of the material is inversely proportional to the square of its radius

In other words:

At constant resistivity and length:

where R stands for resistance and r stands for radius

Now, we are given that the diameter is tripled, this means that the radius id tripled as well.

Substituting in the above equation :

This means that:

New resistance = old resistance / 9

New resistance = 5/9 ohm

3- getting the final current:

Again, using ohm's law, we have:

Voltage is unchanged = 10 volts

Resistance = 5/9 ohm

Therefore:

Hope this helps :)

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