# Validating Ohm's Law With Circuit Simulators

One fundamental experiment that every engineer will need to complete during a lab class is a validation of Ohm’s law using measurements from a real circuit. This act is instructive, but not all engineers will be given an opportunity to conduct the same experiment as a simulation. Should you have the opportunity, a SPICE-based simulator is a good option for simulating circuits and validating Ohm’s law.

SPICE models help you quickly analyze the electrical behavior in a circuit as long as you know the electrical parameters of the elements in the circuit. This will allow you to verify Ohm’s law through simulation, verify Kirchoff’s laws, or calculate the transient behavior of the voltage and current in a circuit.

## Using Circuit Simulators for Validating Ohm’s Law

Ohm’s law is a simple empirical law that relates the conductivity in a material to the current density flowing through it. Most people are familiar with the simple form of Ohm’s law, V = IR. The two formulations are equivalent, although the equation V = IR is used for analyzing circuits.

This equation holds for the overall circuit, where the voltage supplied by a source is equal to the total current multiplied by the resistance of the entire circuit. This allows you to easily reduce a complicated circuit to its Thevenin or Norton equivalent circuit. This equation also holds for individual circuit elements: the current flowing through the circuit element is equal to the voltage drop across the element, divided by the element’s resistance.

A SPICE-based circuit simulator will allow you to calculate the voltage and current in each element of a circuit. Circuits are normally drawn as a schematic and are translated into the code used in the circuit simulator.

You’ll need to specify the resistance values for different elements in the circuit. Once you specify the voltage source in the circuit, the SPICE-based simulator will calculate the current in each element in the circuit. This can also work in reverse; if you are using a current source, you can calculate the voltage drop across each element in the circuit. You can then compare these calculations with measurements from an identical circuit and verify the validity of Ohm’s law.

## Going Further: Validating Kirchoff’s Laws

Everyone likes to focus on Ohm’s law in circuits as it is seen as a fundamental result for any circuit. The two other fundamental laws for electrical circuits are Kirchoff’s voltage law and Kirchoff’s current law.

The voltage law makes a statement about conservation of energy in a circuit. If you remember the definition of conservative forces, and the electric field is a conservative force, the sum of changes in energy between multiple points along a loop will add up to zero. In terms of the voltage sources and drops in a circuit, the sum of voltage sources must be equal to the sum of voltage drops around a loop in an electric circuit.

The current law is really just a statement about conservation of electric charge. Just like with fluid flowing in a pipe that splits at a junction, the total charge that flows into a junction is equal to the total charge that flows out of a junction. In other words, charge is neither created nor destroyed in an electric circuit. Thanks to the definition of derivatives, this statement applies to electric currents, i.e., electric currents are conserved.

A SPICE-based simulator naturally lends itself to verifying Kirchoff’s laws because the simulator will need to calculate the voltage drop and current in each element in the circuit. You will already use these to verify Ohm’s law, so you can immediately use these results to verify Kirchoff’s laws through calculation.

*Model for a simple audio amplifier circuit*

## Nonlinear Circuit Elements and Time Dependence

While most simple experiments with Ohm’s law only considers the fundamental linear passive elements (resistors, capacitors, and inductors), circuit simulators can also be used with circuits that contain nonlinear passive circuit elements. A perfect example is a circuit with a diode. The current output from a diode is a nonlinear function of the voltage drop across the diode.

In terms of Ohm’s law, you can use the calculated output current to calculate the forward or reverse resistance of a diode as a function of input voltage. If you have another element in the circuit, like a series resistor, you can use the calculated resistance of the diode and Kirchoff’s laws for validating Ohm’s law.

SPICE-based simulators can also be used for transient analysis or time-dependent simulations. For example, you can examine the behavior of an AC circuit driven with a harmonic voltage source. When working with circuit elements that take some time to rise to their final output current, you can examine the transient behavior of these circuits. This is useful when examining the behavior of a nonlinear circuit element driven with digital pulses.

In both cases, you can use Ohm’s law to describe the impedance of the circuit element in the frequency domain based on the voltage and current in the time domain. This means that SPICE-based simulators work naturally with circuits that contain capacitors and inductors, and you can determine the total impedance in the circuit as a function of frequency.

With the right circuit simulation and analysis package, you can verify the fundamental laws of electric circuits or analyze complex boards filled with a mix of linear and nonlinear devices. An adaptable program like the PSpice Designer for OrCAD will remain useful as your designs become more complex. This unique tool takes data directly from your schematic and/or PCB, giving you a full view of the behavior of your circuits.

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