 ## Basic Electrical Circuits

The Electrical Theory playlist from Khan Academy contains a series of videos that walks through different electrical circuits, Ohm’s Law, Kirchhoff’s laws, and much more! If you are looking for additional resources, there are more listed below for each topic.

Here are some important terms to know:

Charge: In electrical terms, charge refers to the fundamental property of matter responsible for electric interactions. It is denoted by the symbol “Q” and is measured in units called coulombs (C). Think of charge as the “currency” of electricity. Just as money can be positive or negative, charge can also be positive or negative.

Current: It is the flow of electric charge through a conductor and is denoted by the symbol “I.” Electric current is measured in units called amperes (A). One ampere is equivalent to one coulomb of charge flowing per second.

Current can be calculated via the following formula:

Where:

Q = quantity of charge in coulombs (C)

I = current in amperes (A)

T = time in seconds (s)

Resistance: This is the opposition or hindrance that a material offers to the flow of electric current. It is denoted by the symbol “R” and is measured in ohms (Ω). Resistance determines how current will flow through a conductor.

Voltage: It is the amount of electrical potential energy per unit charge. When there is a voltage difference across a conductor, it creates an electric field that exerts a force on charged particles, such as electrons. This force causes the charges to move, resulting in the flow of electric current. Voltage is denoted by the symbol “V” and is measured in units called volts (V).

Electromotive Force (EMF): This is a term often used interchangeably with voltage, but they are slightly different concepts. EMF is the electrical energy per unit charge supplied by a source such as a battery or a generator. It represents the work done by the source to move charge through a circuit. EMF is measured in units of volts (V), just like voltage. EMF is responsible for establishing the potential difference, or voltage, across a circuit.

### Ohm’s Law

Ohms Law is a basic principle that explains how electricity behaves in a circuit. It says that the amount of current (I) flowing through a circuit is directly proportional to the voltage (V) and inversely proportional to the resistance (R) of the circuit. The equation for Ohm’s Law is as follows:

Ohms Law tells us that if we increase the voltage in a circuit, the current will increase as well, and if we increase the resistance, the current will decrease.

Think of it like a water pipe: voltage is like water pressure, current is like the flow of water, and resistance is like a narrow section of the pipe that restricts the flow. If you increase the water pressure (voltage), the flow of water (current) will increase as well, and if you add a narrow section to the pipe (resistance), the flow of water will decrease.

### Kirchoff's Laws

Kirchhoff’s current law (KCL) states that the total current entering a node (or a junction) in an electrical circuit must equal the total current leaving that node. This is because charge is conserved in a closed circuit.

Mathematically, KCL can be written as:

Where Σ I (in) is the sum of all currents entering the node, and Σ I (out) is the sum of all currents leaving the node.

I = Current

Kirchhoff’s Voltage Law (KVL): The total voltage around a closed loop in a circuit must equal zero. This is because energy is conserved in a closed circuit. Mathematically, KVL can be written as:

where Σ V (loop) is the sum of all voltage drops (or rises) around the loop.

For practice, check out this link Kirchhoff’s Laws with Practice Questions

### Series Circuits

In a Series Circuit, all components (such as resistors, capacitors, and inductors) are connected in a single path, so that the same current flows through each component. The components are arranged in such a way that the output of one component is the input of the next component. This means that the voltage across each component can be different, but the current through each component is the same.

In a series circuit, the total resistance is equal to the sum of the individual resistances of each component. This means that as more resistors are added in series, the total resistance of the circuit increases. The total voltage of the circuit is equal to the sum of the individual voltages of each component.

Use this table as a guide for the different formulas or principles that are followed in a series circuit:

 Current (I) IT = I1 = I2 = I3 …. = In Resistance (R) RT = R1 + R2 + R3 …. + Rn Voltage (V) VT = V1 + V2 + V3 …. + Vn

### Parallel Circuits

In a Parallel Circuit, components are connected in such a way that there are multiple paths for the current to flow. This means that the voltage across each component is the same, but the current through each component can be different.

In a parallel circuit, as more resistors are added, there are more paths for the current to flow, which decreases the overall resistance. The total voltage of the circuit is the same as the voltage across each individual component.

Use this table as a guide for the different formulas used in a parallel circuit:

 Current (I) IT = I1 + I2 + I3 …. + In Resistance (R) 1/RT = 1/R1 + 1/R2 + 1/R3 …. + 1/Rn Voltage (V) VT = V1 = V2 = V3 …. = Vn

### Series-Parallel Circuits

In a Series-Parallel Combined Circuit, some components are connected in series, while others are connected in parallel.

The total resistance of a series-parallel circuit depends on the arrangement of the components. The total voltage of the circuit is equal to the voltage across each individual component. The current through each component depends on its position in the circuit. Components in the series portion of the circuit share the same current, while components in the parallel portion of the circuit have different currents.

Use this table as a guide for the different formulas used in a parallel circuit:

### Edison 3-Wires

An Edison 3-Wire distribution system uses three conductors. Two of the conductors have equal, but opposite potential; where one is positive and the other is negative. The other conductor is neutral (typically at ground potential). The neutral conductor provides a return path for the current flowing through the non-neutral conductors, and it helps balance the voltage between them.

Check out these resources for a further explanation on how to solve Edison 3-wire problems:

Some content from the Trades Science webpage was generated using ChatGPT.

OpenAI. (2023). ChatGPT (Mar 14-July 10 version) [Large language model]. https://chat.openai.com/chat