Electric Circuits Legacy Problem #29 Guided Solution

In approaching series and parallel circuit problems, one of the first decisions which you must make when reading a problem is to decide Are the resistors in the circuit connected in series, or are they connected in parallel? Because the mathematics and concepts that pertain to these two types of circuits depend on what type of circuit it is It's different for a series circuit as it is for a parallel circuit. Here very clearly they describe the circuit as being a parallel arrangement of two resistors And they ask us to find the equivalent resistor of this arrangement of two resistors In other words if you were to snap out those two resistors and replace it with a single resistor What resistance must that resistor have in order for its resistance to be Equivalent to the combination of the two resistors. That's what we mean by equivalent resistance Now in order to find the equivalent resistance for parallel arrangement resistors, you need to use this equation. It's complicated You'll find it in the overview page to the set of problems. It goes like this 1 over R equivalent equal 1 over R 1 plus 1 over R 2 And if there were a third resistor you'd add plus 1 over R 3 So we have two resistors here, and what I can say is 1 over the equivalent resistance Is equal to 1 over one of the resistance values plus 1 over the other resistance value I'm going to drop down the part D of this problem, and I'm going to as examples do those two Do part D and maybe E or F. So in part D I'm going to write this statement 1 over R equivalent equal 1 over 5 plus 1 over 9.2 Now I pull out my calculator, and I evaluate the right side of the equation I go 1 over 5 or 1 divided by 5 Plus 1 divided by 9.2 Enter or equal and I find out what that is and it comes out to be 0.3087 Now that's not my answer to part D because the equation says on the left side 1 over R equivalent Is equal to the right side which we've evaluated to be 0.3087 Using our calculator now to find the left side of the equation I have to take the reciprocal of it And I have to take the reciprocal on the right side of the equation Taking the reciprocal on the left side of the equation becomes R equivalent That's what I'm looking for now taking the reciprocal on the right side of the equation I take the reciprocal of 0.3087 1 divided by the number on my calculator And I get 3.2394 ohms. That's my answer to part D I round that to a single decimal place or two significant digits Now on part E I'll do one more example. I'm going to do the same thing I'm going to say 1 over R equivalent is equal to 1 over 5.0 plus 1 over 27.1 ohms Now I'm going to evaluate the right side of that equation on my calculator 1 divided by 5 plus 1 divided by 27.1 equal or enter And I end up getting 0.2369 and that's not the answer again Because the equation says 1 over R equivalent is equal to 0.2369 Now you can reciprocate both sides. Reciprocating the left side gives you R equivalent And reciprocating the right side or taking 1 divided by 0.2369 gives you 4.2212 ohms I can round that to a single decimal place or two significant digits and I have my answer