Practice problems for these concepts can be found at:

Circuits Practice Problems for AP Physics B & C

Here it is—the trick that will make solving circuits a breeze. Use this method on your homework. Use this method on your quizzes and tests. But most of all, use this method on the AP exam. It works.

The easiest way to understand the *V*-*I*-*R* chart is to see it in action, so we'll go through a problem together, filling in the chart at each step along the way.

We start by drawing our V-I-R chart, and we fill in the known values. Right now, we know the resistance of each resistor, and we know the total voltage (it's written next to the battery).

Next, we simplify the circuit. This means that we calculate the equivalent resistance and redraw the circuit accordingly. We'll first find the equivalent resistance of the parallel part of the circuit:

Use your calculator to get

Taking the reciprocal and rounding to 1 significant figure, we get

*R*

_{eq}= 4 Ω

So we can redraw our circuit like this:

Next, we calculate the equivalent resistance of the entire circuit. Following our rule for resistors in series, we have

*R*

_{eq}= 4 Ω + 5 Ω = 9 Ω

We can now fill this value into the *V*-*I*-*R* chart.

Notice that we now have two of the three values in the "Total" row. Using Ohm's law, we can calculate the third. That's the beauty of the *V*-*I*-*R* chart: *Ohm's law is valid whenever two of the three entries in a row are known*.

Then we need to put on our thinking caps. We know that all the current that flows through our circuit will also flow through *R*_{1} (You may want to take a look back at the original drawing of our circuit to make sure you understand why this is so). Therefore, the *I* value in the "*R*_{1}" row will be the same as the I in the "Total" row. We now have two of the three values in the "*R*_{1}" row, so we can solve for the third using Ohm's law.

Finally, we know that the voltage across *R*_{2} equals the voltage across *R*_{3}, because these resistors are connected in parallel. The total voltage across the circuit is 12 V, and the voltage across *R*_{1} is 6.5 V. So the voltage that occurs between *R*_{1} and the end of the circuit is

- 12 V – 6.5 V = 5.5 V.

Therefore, the voltage across *R*_{2}, which is the same as the voltage across *R*_{3}, is 5.5 V. We can fill this value into our table. Finally, we can use Ohm's law to calculate *I* for both *R*_{2} and *R*_{3}. The finished *V*-*I*-*R* chart looks like this:

To answer the original question, which asked for the voltage across each resistor, we just read the values straight from the chart.

Now, you might be saying to yourself, "This seems like an awful lot of work to solve a relatively simple problem." You're right—it is.

However, there are several advantages to the *V*-*I*-*R* chart. The major advantage is that, by using it, you force yourself to approach every circuit problem exactly the same way. So when you're under pressure—as you will be during the AP exam—you'll have a tried-and-true method to turn to.

Also, if there are a whole bunch of resistors, you'll find that the *V*-*I*-*R* chart is a great way to organize all your calculations. That way, if you want to check your work, it'll be very easy to do.

Finally, free-response problems that involve circuits generally ask you questions like these.

- What is the voltage across each resistor?
- What is the current flowing through resistor #4?
- What is the power dissipated by resistor #2?

By using the *V*-*I*-*R* chart, you do all your calculations once, and then you have all the values you need to solve any question that the AP writers could possibly throw at you.

### Tips for Solving Circuit Problems Using the *V*-*I*-*R* Chart

- First, enter all the given information into your chart. If resistors haven't already been given names (like "
*R*_{1}"), you should name them for easy reference. - Next simplify the circuit to calculate
*R*_{eq}, if possible. - Once you have two values in a row, you can calculate the third using Ohm's law.
*You CANNOT use Ohm's law unless you have two of the three values in a row*. - Remember that if two resistors are in series, the current through one of them equals the current through the other. And if two resistors are in parallel, the voltage across one equals the voltage across the other.

Practice problems for these concepts can be found at:

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