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3 years ago

Help me with questions 1-8. here's the link to the textbook

Physics

1 answer:

SVETLANKA909090 [29]3 years ago

5 0

Ok so basically I’m here for the points cuz I gotta quiz do in 10 minutes sorry

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Tungsten has a temperature coefficient of resistivity of 0.0045 (c°)-1. a tungsten wire is connected to a source of constant vol

Murljashka [212]

Answer:

$131.1^{\circ}C$

Explanation:

The power delivered in the wire is given by:

$P=\frac{V^2}{R}$

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:

$V^2 = PR=const.$ (1)

At the beginning, the initial resistance is $R_0$ , and the power delivered is $P_0$ . Later, when the temperature increases, the power becomes $P_1 = \frac{2}{3}P_0$ , and the new resistance is $R_1$ . Using (1), we can write

$P_0 R_0 = \frac{2}{3}P_0 R_1\\R_1 = \frac{3}{2}\frac{P_0 R_0}{P_0}=\frac{3}{2}R_0$ (2)

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

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

$R_1 = R_0 (1+\alpha \Delta T)$

where

$\alpha = 0.0045 ^{\circ}C^{-1}$ is the temperature coefficient

$\Delta T$ is the change in temperature

Using (2), we can rewrite this equation as

$\frac{3}{2}R_0 = R_0(1+ \alpha \Delta T)$

and we find:

$\frac{3}{2}=1+\alpha \Delta T\\\Delta T=\frac{\frac{3}{2}-1}{\alpha}=111.1 ^{\circ}$

So, the new temperature of the wire must be

$T_f = 21^{\circ}+111.1^{\circ}=132.1^{\circ}$

6 0

3 years ago