Tungsten has a temperature coefficient of resistivity of 0.0045 (c°)-1. a tungsten wire is connected to a source of constant voltage via a switch. at the instant the switch is closed, the temperature of the wire is 21 °c, and the initial power delivered to the wire is p0. at what wire temperature will the power that is delivered to the wire be decreased to 2/3 p0?

Explanation:

The power delivered in the wire is given by:

where V is the voltage of the battery and R is the resistance of the wire.

Since the voltage of the battery is constant, we can rewrite this equation as follows:

(1)

At the beginning, the initial resistance is , and the power delivered is . Later, when the temperature increases, the power becomes , and the new resistance is . Using (1), we can write

(2)

So, the new resistance must be 3/2 of the initial resistance.

We know that the resistance increases linearly with the temperature, as

where

is the temperature coefficient

is the change in temperature

Using (2), we can rewrite this equation as

and we find:

So, the new temperature of the wire must be