You should now have the answers to question #1 and #2 on the back. I left #3 and #4 for you to continue working on your own.
Equivalent Resistance
Learning Goals: Understand how to calculate equivalent resistance.Success Criteria: You can successfully calculate the equivalent resistance for series and parallel circuits.
We began by looking at this picture:
Handout: Equivalent Resistance
We looked at two circuits with resistors. What is the equivalent resistance? Asking for the "equivalent resistance" is the same thing as asking for the "total resistance".
Series
In series the total resistance is the SUM of each resistor.
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So in this case we have,
The equivalent resistance is 6 Ω.
Parallel
In parallel the total resistance is the RECIPROCAL SUM of the each resistor.
So in this case we have,
Notice the step where we had to flip over both sides of the equation. We must do this because the answer needs to have R total and Ohms on top.
Notice that we used the same three resistors. The total resistance in series is 6 Ω, but the total in parallel is only 0.5 Ω, much less than any of the resistors on their own! Why is this the case? Look at this image:
Imagine the wires are roads and electrons are cars. Adding a resistor is like adding a toll booth. It slows down the cars passing through. If there are three toll booths in a row, every electron has to go through all three tolls, slowing everyone down. If there are three toll booths in parallel, cars can choose which one to go through and traffic flows a lot smoother.
In the same way, resistors in parallel have less equivalent resistance allowing more current. That's why light bulb in parallel shine brighter!
Homework: Complete the rest of the handout. Notice there are some circuits that are a combination of series and parallel!
Solutions to the first 4 questions:
- RT = 13 Ω
- RT = 4.6 Ω
- RT = 4.65 Ω
- RT = 4.3 Ω
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