NTC thermistor heat dissapation calculation with graphs

[theanswerai]

Homework Statement

The attached graph_1 represents the resistance R of a specific NTC thermistor as a function of its temperature ϑ. In the attached graph_2, the heat dissapation P of the thermistor at room temperature of 22 ˚C is displayed as a function of temperature of the thermistor.

Determine the maximum voltage that may be applied to the thermistor to prevent it from heating up above 65 ˚C!

Assume that the thermistor is initially at room temperature.

Relevant Equations

heat dissapation

I couldn't solve this problem. Any tips or help would be appreciated. If I am violating against any rules please comment, as this is my second post :-).

 

[berkeman]

Homework Statement:: The attached graph_1 represents the resistance R of a specific NTC thermistor as a function of its temperature ϑ. In the attached graph_2, the heat dissapation P of the thermistor at room temperature of 22 ˚C is displayed as a function of temperature of the thermistor.

Determine the maximum voltage that may be applied to the thermistor to prevent it from heating up above 65 ˚C!

Assume that the thermistor is initially at room temperature.
Relevant Equations:: heat dissapation

I couldn't solve this problem. Any tips or help would be appreciated. If I am violating against any rules please comment, as this is my second post :-).

Both graphs have Temperature on the horizontal axis. Draw vertical lines on the two graphs at 65C -- What two datapoints does that give you? How can you then use those two datapoints to determine the maximum applied voltage?

 

[theanswerai]

The graph reveals that the power dissapated must be about 320 mW. The resistance at 65°C is about 115 Ω. Now we can simply plug in these values: $$V²=P*R⇒V=√PR⇒V=√36.8≈6V$$
Is this correct? I am not sure because this is how to calculate the voltage for a resistor and in this problem we have a thermistor...

 

[berkeman]

Looks good to me. A thermistor is just a resistor with a high thermal coefficient of resistance. So when it stabilizes, it just looks like a resistor as long as the voltage across it is not changing.

 

[theanswerai]

Thanks a lot for your help!