/sci/ - Science & Math

>>11351211
First:
>resistors in short circuit
I don't think that makes sense. Short circuits have no resistance, by definition. You would never intentionally build a short circuit in a basic physics/circuits lab.
>Resistivity is directly associated with temperature, so an increase in temperature means higher resistance
Not necessarily true. Ceramics and semiconductors have a negative temperature coefficients (decreased resistivity at higher temps.) while metals all have positive coefficients (more resistive at higher temp.). Thermistors are resistors that are specifically designed to exploit this phenomenon and are used in sensors, and can have negative or positive coeffs.

Experiment:
Let's say we have a simple circuit with a 9 volt battery in series with 1 kohm ceramic resistor. If we measure the current at the spec. temperature for the resistor, we get a current of about 9 mA. US Resistor, the manufacturer of our resistor, rates the thing with a temp. coefficient of about [math] \alpha=-0.0002\ ^\circ\text{C}^{-1}[/math]. http://www.usresistor.com/index.php/materials/ceramic-resistors
The exact equation that models this is
[eqn] \frac{\text
{d}R}{R}=\alpha\text{ d}T [/eqn]
However, usually we can assume that [math] \alpha [/math] is a constant and [math] R [/math] doesn't change very much with temperature. Someone comfortable truncating a Taylor expansion after the first term would get the following approximation. Say we remove and heat the resistor by 200°C in an oven before replacing:
[eqn] \Delta R=R_0\alpha\Delta T=(1\text{ k}\Omega)(-0.0002\ ^\circ\text{C}^{-1})(200\ ^\circ\text{C})=-40\ \Omega [/eqn]
So our new resistance is [math] R'=1000+\Delta R=960\ \Omega [/math] and the new current in your circuit is [math]9/960=9.375\text{ mA}[/math] which is greater than before. The voltage is exactly the same because our power source did not change, but the resistance and current did.
>>11351511
You've got to be patient, lover.