Understanding Electrical Circuits, Resistance, and Ohm’s Law

Posted on Aug 26, 2024 in Physics

Electric Circuits: Concepts and Applications

An electrical circuit is a group of elements connected to each other in which a transference and transformation energy process is created by the motion of electric charges.

An electrical circuit is formed by the following elements:

Elements of an Electrical Circuit

Loops: Closed trajectory in a circuit.
Net: Closed trajectory that does not have another closed trajectory inside.
Nodes: Connection between 2 or more electrical elements.
Branch: Any electrical element or group of elements connected between 2 nodes.

Example 8.1

In the next figure, determine how many loops, nets, and nodes there are:

Answer:

3 loops	ABEF, ABCDEF, BCDE
2 nets	ABEF, BCDE
4 nodes	A, B, C, E

The sources that provide power on a circuit can be dependent or independent. In this topic, we will focus on independent sources, which have a constant magnitude.

Electric Current (I)

Electric current (I) is defined as the flow of charge through a conductor. It has a magnitude, direction, and type (direct or alternating current). There must be a closed circuit for the current to flow. Its unit of measurement is the Ampere (A [=] C/s).

Electric Voltage (V)

Electric voltage (V) is the required energy for the current to flow. It has a magnitude and polarity (+ or –). Its unit of measurement is the Volt (V).

Electric Power (P)

Electric power (P) is the speed at which an element consumes or provides energy. Its unit of measurement is the Watt.

If the current flows through the positive sign (+), the energy is consumed; if the energy flows through the negative sign (–), it is provided.

Example 8.2

Calculate the power of the following elements and state if power is consumed or provided.

Answer:

A		Provides power
B		Consumes power
C		Provides power, because when the current has a negative sign, it means it flows in the opposite direction.

Direct Current and Alternating Current

Direct Current (DC)

Direct current (DC) is when the voltage always maintains the same polarity (signs do not change). Examples of this type of current can be seen in batteries, whose positive and negative terminals are always, respectively, positive and negative. This means that current always flows in the same direction between those two terminals.

Alternating Current (AC)

An alternating current’s (AC) polarity changes constantly every certain cycles of time. For example, the power that comes from a power plant is called alternating current (AC). The direction of the current reverses, or alternates, 60 times per second (in the U.S. and Mexico) or 50 times per second (in Europe). The power that is available at a wall socket in Mexico is 110-volt, 60-cycle AC power.

Electric Resistance: Concepts and Calculations

An electric resistance (R) is the opposition to charge flow through a circuit. Its unit of measurement is the Ohm (Ω), represented as follows:

All metals, despite being fair conductors, possess certain opposition to the charge flow passing through.

Resistances can be connected in series or in parallel.

Resistances in Series

When resistances are connected in series, the electric current is the same for all.

Resistances in Parallel

When resistances are connected in parallel, the voltage is the same in each resistance.

Resistivity (ρ)

Resistivity (ρ) is the proportionality constant between resistance and the quotient between length and area. It is a property of matter, and its unit of measurement is the Ω m.

Where l is the conductor’s length and A the area of its transversal section.

Example 9.1

What would be the length of a silver wire of 0.05 cm in diameter if we want to create a 7 Ω resistance?

Ohm’s Law

Ohm’s Law explains the relation between voltage and current intensity on a passive element. It states that the current that flows through a conductor is directly proportional to the potential difference between its ends. Mathematically, it is expressed as follows:

Example 9.2

The voltage in a certain circuit is 37V when a current of 13A flows through it. What would happen to the current if the voltage were to be decreased by half?

With Ohm’s Law, we obtain the value of the resistance within the circuit:

Now, if the voltage were to be decreased by half, meaning that the new voltage is 18.5V, the current would result as follows:

Serial and Parallel Resistances

Ohm’s Law in Resistances Connected in Series

When there are two resistances connected in series, as in the picture below, the current that flows through R1 is the same that flows through R2.

Using Ohm’s Law, we have that:

The resulting voltage would be the sum of , therefore: . This formula shows us how the value of an equivalent resistance can be obtained when resistances are connected in series:

And the formula for Ohm’s Law would be:

Ohm’s Law in Resistances Connected in Parallel

When there are two resistances connected in parallel, as in the picture below, the voltage in both is the same, , and the resulting flow would be the sum of both currents.