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# Resistors in Series and in Parallel for AP Physics B & C

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By McGraw-Hill Professional
Updated on Feb 12, 2011

Practice problems for these concepts can be found at:

Circuits Practice Problems for AP Physics B & C

In a circuit, resistors can either be arranged in series with one another or parallel to one another. Before we take a look at each type of arrangement, though, we need first to familiarize ourselves with circuit symbols, shown in Figure 21.3.

First, let's examine resistors in series. In this case, all the resistors are connected in a line, one after the other after the other:

To find the equivalent resistance of series resistors, we just add up all the individual resistors.

For the circuit in Figure 21.4, Req = 3000 Ω. In other words, using three 1000 Ω resistors in series produces the same total resistance as using one 3000 Ω resistor.

Parallel resistors are connected in such a way that you create several paths through which current can flow. For the resistors to be truly in parallel, the current must split, then immediately come back together.

The equivalent resistance of parallel resistors is found by this formula:

For the circuit in Figure 21.5, the equivalent resistance is 333 Ω. So hooking up three 1000 Ω resistors in parallel produces the same total resistance as using one 333 Ω resistor. (Note that the equivalent resistance of parallel resistors is less than any individual resistor in the parallel combination.)

### A Couple of Important Rules

Rule #1—When two resistors are connected in SERIES, the amount of current that flows through one resistor equals the amount of current that flows through the other resistor(s).

Rule #2—When two resistors are connected in PARALLEL, the voltage across one resistor is the same as the voltage across the other resistor(s).

Practice problems for these concepts can be found at:

Circuits Practice Problems for AP Physics B & C

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