Electric Circuits Legacy Problem #20 Guided Solution

Two resistors, which are connected in series, are connected in such a manner that any charge that goes through the first resistor will also go through the second resistor, and as such the overall resistance of the two resistors is actually the sum of the individual resistances of the single resistors. So if you put two resistors of 6 ohms and 8 ohms in series, the overall resistance would be 14 ohms. When we speak of the concept of equivalent resistance, what we're speaking of is if you were to replace those two resistors by a single resistor, what would be the equivalent resistance of that single resistor? In this case, 14 ohms. The equation to remember for series circuits, or series connections of resistors, is that the total resistance, or overall resistance, or equivalent resistance, is simply equal to R1 plus R2 plus however many R's there are. Now the situation is a little more complicated for parallel connected resistors, because in parallel connected resistors, any charge that goes through one of the resistors does not go through the other one. And so not all the charge goes through the 6 ohm resistor, and not all the charge goes through the 8 ohm resistors. The overall effect of this is that the total resistance, or overall resistance, of the set of two resistors is actually going to be less than the individual resistances of the resistors, since not all the charge is going through those resistors. The mathematics for calculating the equivalent resistance goes like this. 1 over R equivalent is equal to 1 over R1 plus 1 over R2. It's based on a reciprocal addition. So to find the overall resistance, you're going to have to plug 6 and 8 ohms into the equation for R1 and R2. So I would write this down. It would become 1 over R equivalent is equal to 1 over 6 plus 1 over 8. Now you can carry this out on your calculator, or with the numbers being as easy as they are, you could find the lowest common denominator and add the two fractions on the right side of the equation. The lowest common denominator becomes 24, so 4 over 24 plus 3 over 24 would be how you translate that. That's 7 over 24. And when you've got that, that's not the answer to the question. If you look at your equation, that's equal to 1 over the equivalent resistance. So if I want to find the equivalent resistance, I have to reciprocate both sides of the equation such that the equivalent resistance is now 24 over 7, which comes out to be 3.428 ohms. You can round that to two significant digits, and it's 3.4 ohms. I gave you the fraction method of doing this. You can simply do this on your calculator as well. Type in 1 divided by 6 plus 1 divided by 8 equal. When you're done, again, you don't have the answer. You have to take the reciprocal of that, since our equation is based on reciprocals. 1 over r is equal to that number on your calculator. Reciprocating it gives you 3.4286.