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Resistance

After talking about current and voltage we now need to consider resistance. We already said that a light bulb added in series represents and obstacle. If such an obstacle is added in series the resistance goes up and the current goes down. That means that current and resistance are inversely proportional. There are several analogies for this concept, ranging from hurdles put into the path of a runner to tollbooths on a highway. We also found that voltage is proportional to resistance. If voltage is the push that pushes the current through a circuit then this also makes sense because if you consider a revolving door that hasn’t been greased in a  long time (it has a high resistance) in order to get the same current (number of people moving through the door per minute) each person needs to push harder to get through to make the door move. And also the more push there is (and the resistance is constant) the more current there will be.

 

 

To sum up: we have current inversely proportional to resistance, current proportional to change in voltage and change in voltage proportional to resistance. Putting this all together leads to Ohm’s law.

One more thing that is important is to find out how to calculate the total resistance of a circuit. This is important because the battery sends out a current based on the total resistance that it is hooked up to. The battery only “sees” this total, or equivalent, resistance. If two resistors are in series this is very straightforward, they are simply added together. This makes sense because the adding something in series increases the resistance as we learned in the very first class. A 10 Ohm and a 15 Ohm in series have a total of 25 Ohm. If two resistors are in parallel things change, because adding a resistor in parallel decreases the total resistance.

 

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Consider the situation above to the left. If the resistors were light bulbs we know that each light bulb would get the same current. Not only this but they would also get the same current as one light bulb alone hooked up to the same battery. If this is not clear, go back to the second page of the first tutorial. That means that adding a light bulb in parallel doubles the current through the battery. In order for the current to double the resistance has to get cut in half. So adding a light bulb in parallel cuts the resistance in half. Adding a third one then decreases the resistance down to a third. A rule could then be that for identical resistors added in parallel the total resistance is R/n or the resistance of each divided by the number of resistors. Two 10 Ohm resistors in parallel have a total resistance of 5 Ohm, three 12 Ohm resistors have a total resistance of 4 Ohm.

What happens when the resistors are not the same? For instance if a circuit has to parallel resistors, one 3 Ohm and the other 6 Ohm. Adding a resistors will decrease the total  

For three identical resitors you simply divide the resitance by three to get the total resitance of the circuit.

 

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