Have you ever held a wire that has current flowing through it? If so what did you notice about it? The wire gets hot. The increase in temperature causes the charge carriers to move faster (increases the internal energy of the charge carriers). If the charge carriers are moving faster what would this say for the time between collisions? The time between collisions  should decrease. If the time between collisions decreases what does this say about the resistance of the material? The conductivity should decrease, therefore the resistivity and hence resistance should increase. A relationship can therefore be determined between resistivity and temperature.  – Final resistivity (  m)  0 – Initial resistivity (  m)  – Temperature coefficient of resistivity (1/ o c) T – Final temperature ( o c) T 0 – Initial temperature ( o c) Since resistance and resistivity are directly related we can obtain a similar expression for resistance as a function of temperature. This is only valid if the length dimensions of the wire do not change!

Example: A section of copper wire has a length of 3 m and a diameter of 0.5 mm. a) What is the resistance of the wire? b) What is the resistance of the wire if the temperature is increased from 20 o c to 100 o c? (  Cu = 3.9x / o c, Assume no thermal expansion). a) b) For thermal expansion:  – coefficient of linear expansion When the wire heats up it means that energy is being transferred from the wire to the environment. What does this mean for the total energy of the circuit? The energy of the circuit should decrease by the amount transferred to the environment. We are then essentially examining the rate at which energy is removed from the circuit. What is another name for this rate? Power. The loss of energy comes from the collisions between the charge carriers in the material and collisions of air molecules with the wire.

How do we relate power to the electric circuit? Energy required to move a charge across a potential difference Current P – Power (W) I – Current (A)  V – Electric potential difference (V) Using Ohm’s Law we can write the power several different ways. Example: A 30 W light bulb operates with this power output when 120 V is applied across the bulb. If the voltage drops by 20 V, what is the power output of the bulb? You cannot use the current since the current changes with the voltage!

Now that we understand the relationship between voltage, current and resistance we can begin putting it all together and examine how these quantities work together in an electric circuit. We know that a simple battery is an electrochemical cell with two electrodes in an electrolyte. Each electrode is connected to one terminal of the battery, with each terminal at a different electric potential. An electric field is present and sets up a potential difference between the two terminals, which forces the charges to move through the wire. The ideal maximum potential difference that can be achieved by the electrochemical cell (or any battery) is called the Electromotive Force (emf). This is not a force it is an electric potential difference, the name is historical. The physical make-up of the electrochemical cell and the electrolyte provides some resistance to the motion of charges prior to leaving the battery. (Resistance due to connectors as well as the electrolyte). Electric potential difference between terminals is the output of the battery emfInternal resistance VV VV

The battery terminal voltage is always less than the ideal emf voltage. How would we determine the terminal voltage from the emf? The total voltage across the battery terminals would be the emf if there was no resistance. What effect does the internal resistance have? The internal resistance (or any resistance) reduces the current by dissipating some of the electrical energy in the form of heat. The loss in energy means that there is a drop in the electrical potential difference between the two sides of the resistor. We should reduce the emf by the drop in the voltage across the resistor. Terminal voltage Voltage drop across resistor  V – terminal voltage (V)  – emf (V) I – current (A) r – internal resistance of battery (  ) If no current flows through the resistor the terminal voltage and the emf are equal. This is the open-circuit potential. Open circuit potential – electric potential difference between two points when there is no current between those points.