Thanks to the physical laws of electronics, circuit analysis is very procedural. This is the second entry in a tutorial in basic electronics. The first entry covered basic electronic concepts such as voltage, current, and power. This session will cover Ohm’s Law, and Kirchhoff’s Laws of voltage and current. These are the fundamental laws needed for circuit analysis and design.

Resistors and Ohm’s Law

Georg Simon Ohm was a German physicist that in 1826 experimentally determined most basic laws that relate to voltage and current for a resistor.

Ohm’s law basically states that the resistance of a component (commonly a resistor) is equal to the voltage dropped over the resistor divided by the current going through it.

This law makes it relatively easy to find one of three values: voltage across a resistance, the resistance value itself, or the current flowing through the resistance (as long as the other two values are known).

Nodes, Branches, and Loops

These three concepts must be understood for basic circuit analysis. They help determine if components are in series or parallel and if the components share the same current or have the same voltage drops.

A branch represents a single circuit component such as a resistor or voltage source.

A node is a point where two or more branches connect.

A loop is any closed path in a circuit.

Elements are in series if they exclusively share a single node. Elements that are in series share the same current.

Elements are in parallel if they are connected to the same two nodes. Elements in parallel have the same voltage across them.

Kirchhoff’s Laws

The first of Kirchhoff’s Laws is Kirchhoff’s current law (KCL). This law states that the sum of all current entering a node or enclosed area of a circuit is equal to zero. Simply put, current entering a node or area equals the current leaving the node or area.

The second of Kirchhoff’s Laws is Kirchhoff’s voltage law (KVL). This law states that the sum of all voltages around a closed path or loop is equal to zero. Simply put, the sum of voltage drops equals the sum of voltage rises.

This is found by following the loop in one direction (the direction does not matter). If the positive terminal is hit first, the voltage is added. If the negative terminal is hit first, the voltage is subtracted. Together these values will equal zero.

Once all of the voltages are found, we can start the loop anywhere we want. I find it convenient to start at the negative terminal of a main voltage source. Since we hit a negative terminal first, we subtract it. Now we simply finish the loop and add the voltages together.

This law comes in very handy for analysis.

Basic DC Analysis

By combining Kirchhoff’s voltage and current laws, basic DC circuits are relatively easy to analyze. Knowing that all voltages in a loop add up to zero and all currents entering a node, minus currents leaving a node also equals zero, most current and voltage values can be easily obtained.

If a loop contains one voltage source and multiple resistances, voltage division (eq. 1) should be used to find the value of voltage drops across the known resistances. Once the voltage across the known resistance is found, Ohm’s law (eq. 2) can be used to determine the current flowing through the resistance.

Eq.1 Voltage Division:

((voltage source in volts) (resistor of interest in ohms))/(sum of resistance in loop)

Eq.2 Ohm’s Law:

(voltage across a resistance) = (known resistance)(current flowing through resistance)

Keep in mind that resistors in series can be added to give total resistance between two nodes. The total resistance between two nodes that have resistors in parallel is found using eq. 3 below.

Eq. 3 Equivalent Resistance (Req) of Resistors in parallel:

Req = ((resistance in branch 1)(resistance in branch 2)) / (sum of resistances in both branches)

There is much more to be said about DC circuit analysis but most would go beyond the scope of this article. The purpose of this article is to give a basic understanding of the laws and concepts of basic electronics.

Other concepts that make DC circuit analysis easier are current division, mesh analysis, and nodal analysis. These techniques use the rules behind KVL, KCL, and Ohm’s Law but would require a visual example for thorough explanation.

I hope that this short tutorial has been helpful to anyone who is new to the world of electronics either as a hobbyist or as a technician trying to learn electronics repair.

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