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# Kirchoff 's Laws 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

Kirchoff 's laws help you solve complicated circuits. They are especially useful if your circuit contains two batteries.

Kirchoff 's laws say:

The first law is called the "junction rule," and the second is called the "loop rule." To illustrate the junction rule, we'll revisit the circuit from our first problem (see Figure 21.6).

According to the junction rule, whatever current enters Junction "A" must also leave Junction "A." So let's say that 1.25 A enters Junction "A," and then that current gets split between the two branches. If we measured the current in the top branch and the current in the bottom branch, we would find that the total current equals 1.25 A. And, in fact, when the two branches came back together at Junction "B," we would find that exactly 1.25 A was flowing out through Junction "B" and through the rest of the circuit.

Kirchoff 's junction rule says that charge is conserved: you don't lose any current when the wire bends or branches. This seems remarkably obvious, but it's also remarkably essential to solving circuit problems.

Kirchoff 's loop rule is a bit less self-evident, but it's quite useful in sorting out difficult circuits.

As an example, we'll show you how to use Kirchoff 's loop rule to find the current through all the resistors in the circuit below.

We will follow the steps for using Kirchoff 's loop rule:

• Arbitrarily choose a direction of current. Draw arrows on your circuit to indicate this direction.
• Follow the loop in the direction you chose. When you cross a resistor, the voltage is –IR, where R is the resistance, and I is the current following through the resistor. This is just an application of Ohm's law. (If you have to follow a loop against the current, though, the voltage across a resistor is written +IR.)
• When you cross a battery, if you trace from the – to the + add the voltage of the battery, subtract the battery's voltage if you trace from + to –.
• Set the sum of your voltages equal to 0. Solve. If the current you calculate is negative, then the direction you chose was wrong—the current actually flows in the direction opposite to your arrows.

In the case of Figure 21.7, we'll start by collapsing the two parallel resistors into a single equivalent resistor of 170 Ω. You don't have to do this, but it makes the mathematics much simpler.

Next, we'll choose a direction of current flow. But which way? In this particular case, you can probably guess that the 9 V battery will dominate the 1.5 V battery, and thus the current will be clockwise. But even if you aren't sure, just choose a direction and stick with it—if you get a negative current, you chose the wrong direction.

Here is the circuit redrawn with the parallel resistors collapsed and the assumed direction of current shown. Because there's now only one path for current to flow through, we have labeled that current I.

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