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Background Information: I'm doing an experiment in which I place a bare tungsten wire in to various liqids, to measure a coefficient $\alpha $ in the equation $$ Power Dissipated = \alpha * \Delta T $$ I was also given the equation: $$R=R_0*(1+0.0045 \Delta T)$$ I decided to measure $R_0$ at a low voltage and current to stop the wire from heating up. Then I placed it in the liquid and measured the current going through the wire for a variety of voltages.

Originally I planed the substitute $Power Dissipated = V*I$ and obtain $R$ from the tangent of a V-I graph (can't use Ohms Law because the situation isn't ohmic) Unfortunately once I have substituted the values into the formulae I got a different value for every data point (all in the same range 10^-7). It made me wonder is there an equivalent formula for non-ohmic power I'm missing or is it something else entirely?

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Have you considered that the $\Delta T$ in your power equation is not the same as the $\Delta T$ in your resistance equation unless the initial temperature of the liquid and the temperature at which you measured $R_0$ are equal? – Pranav Hosangadi Nov 15 '13 at 7:02
up vote 1 down vote accepted

Pranav's comment neatly identifies the problem. The temperature of the wire and the fluid aren't the same, and you don't know the temperature of the wire.

You need to measure $V$ and $I$, then calculate $R$ and use the second equation to calculate the temperature of the wire. Assuming you have a thermometer in your liquid you can now calculate the $\Delta T$ to use in your first equation.

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