20.2

Series and Parallel Circuits

Student Notes

With this simulation, you can create circuits with a battery and up to three resistors. Resistor R1 is shown in red, R2 is in blue, and R3 is in green. The graph shows current versus the battery voltage. Here are some things to investigate: Using Circuit 1, adjust the values of the battery voltage and the resistance of R1. How does the current change? Which law relates the voltage, current, and resistance? Select Circuit 2, where R2 is in series with R1. How does the current through R1 compare with that through R2? What is the relationship between the voltage across R1, the voltage across R2, and the battery voltage? (This is known as Kirchoff's loop rule.) If you now select Circuit 3, which brings in a third resistor R3 in series with the first two, do the same rules apply? Select Circuit 4, with R1 and R2 connected in parallel. How does the voltage across R1 compare with that through R2? What is the connection between the total current in the circuit and the current through the two resistors? (This is known as Kirchoff's junction rule.) If you now add R3 in parallel by selecting Circuit 5, do the same rules apply? Circuits 6 and 7 show the three resistors connected in series-parallel combinations. Investigate these to see how the current through each resistor is related to the total current, and how the voltage across each resistor is related to the battery voltage. Also, calculate the equivalent resistance of each circuit for a particular set of R1, R2, and R3 values - does your value agree with the "Equiv. resistor" readout in the simulation?

Self-test

When a single resistor is connected to a battery, the current through that resistor can be found using Ohm's Law, by dividing the battery voltage by the resistance. With more than one resistor in the circuit this no longer works - you can't find the current through a resistor by dividing the battery voltage by the resistance of the resistor. Why not? Ohm's Law still applies, but how do you use it to find the current? Many people have the mistaken impression that current is used up around a circuit. In a series circuit, for instance, is it true that the current decreases as it passes through the resistors? What actually happens? What is the slope of the current vs. voltage graph for a particular resistor? Consider a situation where a resistor is connected to a battery, and then a second resistor is connected in parallel. Does the voltage and current through the first resistor increase, decrease, or stay the same when the second resistor is added? How can you explain this? The answer to the previous question is based on the simulation's assumption that the battery has no internal resistance. How does the answer change if the battery has a non-negligible internal resistance?

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