Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current Law (KCL)

Why do we care about Kirchhoff's Laws

Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current Law (KCL) allow us to perform analysis of circuits in order to determine what the voltage or current should be at any point in the circuit. This can be extremely useful when it comes time to troubleshoot the circuits you build and test. These laws hold true whether a circuit contains a single loop or hundreds of loops. For simplicity sake we will only go over circuits with a few loops, and will rely on simulation tools such as Multisim for more complex examples.

 

Definition of Kirchhoff's Voltage Law (KVL)

Kirchhoff's Voltage Law (KVL) states that the algebraic sum of all of the voltage rises and drops around a closed loop of a circuit is equal to zero. When using KVL, the direction or polarity of your measurement must be constant for each loop of measurements. It does not matter whether the direction or measurement is clockwise around the loop or counterclockwise around the loop as long as it is consistent for each measurement. This concept is explained in our Basic DC Circuit Measurements video.

 

Definition of Kirchhoff's Current Law (KCL)

Kirchhoff's Current Law (KCL) states that the algebraic sum of all the currents into and out of a point in a circuit is zero.  Another way to say it is that the current going into a node of a circuit is equal to the current coming out of the same node of a circuit. This might not seem very useful when we think of simple series type circuits with a single close loop, but when we get into multiple parallel paths in our circuits, its usefulness will become apparent.

 

Voltage and Current in a Series Resistor Circuit

The circuit shown below includes a 12V DC power supply named V1, three resistors named R1, R2, R3, and a ground. When resistors are placed one after another like this, they are said to be in series. This circuit is being simulated in Multisim by National Instrument, and virtual multi-meters XMM1, XMM2, XMM3) are being used to measure the voltage across each resistor. A fourth multi-meter (XMM4) is being used to measure the current flowing through the circuit. The fifth multimeter (XMM5) is being used to measure the voltage across the power supply. Notice the polarity of each multimeter measurement.  If we were to go around this circuit loop clockwise, the positive terminal of the multimeter is at the leading edge of each component in the loop and the negative terminal is on the trailing.  With all measurements around the loop having the same direction we have measured results of 2V, 4V, 6, and -12V.  The sum of these equals zero as KVL states.

Multisim simulation of resistors in series showing the voltage across each resistor and the current flowing through the circuit.

Voltage and Current in a Parallel Resistor Circuit

The circuit shown below includes the same components as the series resistor circuit shown above except the resistors are now placed parallel to each other instead of being in series. This creates three closed loops in the circuit. From left to right we have one loop formed with V1 and R1, one with R1 and R2 loop 2, and one with R2 and R3 loop 3.  In each of these loops we have one component with +12V potential and one with -12V potential.  +12V - 12V - 0V just as KVL states.  In this circuit we can also see KCL at work.  In this example we have three branches represented by each resistor.  Each branch has its own current.  Notice how that the sum of the three branches, 12 mA + 6 mA + 4 mA, is equal to the total current measurement of 22 mA shown by XMM6.

This simulation of a parallel resistor circuit demonstrates Kirchhoff's Voltage law and Kirchhoff's Current Law.

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