The total amount of electric current entering any junction of a circuit must equal the total amount of current leaving that junction. This is known as Kirchhoff’s current law, also known as Kirchhoff’s first law, named after the German physicist Gustav Robert Kirchhoff (1824– 1887). In the example on the right 40 mA enters a junction. If 10 mA leaves by one branch, then 30 mA must leave by the second branch to satisfy Kirchhoff’s current law.
Conservation of charge
Kirchhoff’s current law reflects a fundamental conservation law in physics: the law of conservation of charge. The law of conservation of charge says that the total electric charge of the universe is constant. If two positive charges go in, then two positive charges must also come out, much as every car that enters an intersection must be matched by one that leaves. We will explore electric charge more deeply in Chapter 18.
Kirchhoff’s first law and parallel circuits
Kirchhoff’s first law is usually brought up when discussing parallel circuits, because the total current (here labeled I) splits at one junction and merges at another. Current can only change at junctions, and it does not change when passing through a battery or resistor. In applying Kirchhoff’s law to this parallel circuit, we first apply Ohm’s law to each resistor individually. Next, we add the currents through each resistor to get the total current. Finally, we apply Ohm’s law to the circuit as a whole to obtain the total resistance.
Kirchhoff’s first law and series circuits
But Kirchhoff’s first law is equally important in considering series circuits. Such circuits have no forks in the road, from the perspective of the moving charges—particles do not split off from one another and go in separate directions as current flows through a series circuit. Nevertheless, Kirchhoff’s first law helps us see that the current through each resistor is the same in a series circuit. That insight is essential to solving for the total resistance of such a circuit.
Test your knowledge
As demonstrated on page 490, we used the principle of charge conservation to derive the formula for total resistance in a parallel circuit. The steps were the following:
Apply Ohm’s law (in the form I = V/R) to each resistor individually.
Add the currents through each resistor to get the total current.
Apply Ohm’s law (in the form R = V/I) to get the total resistance.
Which of the above-listed steps is a statement of Kirchhoff’s first law?
1 only
2 only
1 and 3 only
1, 2, and 3
The answer is b (only Step 2 can be equated with Kirchhoff’s first law). The reason is that Kirchhoff’s first law tells us to equate the sum of the currents entering a junction with those exiting that junction. Step 1 uses Ohm’s law to determine the individual currents exiting a junction, and Step 3 already makes use of a single value for total current. Step 2 is where those currents are added to tell us the total amount of current flowing into the resistor network.
The total amount of electric current entering any junction of a circuit must equal the total amount of current leaving that junction. This is known as 
Kirchhoff’s first law is usually brought up when discussing 
But Kirchhoff’s first law is equally important in considering 
