Electrical energy can be dissipated in the form of heat when voltage is applied across a resistor. The magnitude of the voltage across the resistor, also called the driving voltage, and the resistivity of the material that makes up the resistor determine how much heat is generated.

Resistors are designed to **promote thermal energy transfer** from electrical energy. This is why they are manufactured with a specific resistivity material. The higher the resistivity, or **higher resistance per unit length**, the more *thermal energy transfer occurs*.

By designing resistors with high resistivity materials, less driving voltage is needed to *generate enough thermal energy transfer* to dissipate electrical energy as heat. This is very useful in applications where there is limited available voltage to drive it with!

Did you know that there are different ways to measure resistance? In this article, we will discuss how resistance is measured in the International System of Units (SI) and how this measurement applies to wires and cables.

## Calculate resistance of resistor

The *voltage drop across* a resistor is equal to the power dissipated in the resistor divided by the voltage across the resistor.

That is, V= P/V, where P is the power dissipated in the resistor and V is the voltage across the resistor. This can be rearranged to solve for P, or power.

When working with circuits that *contain multiple resistors*, it can be difficult to determine the total power being used by all of the components. This is because it does not account for energy lost in other components.

Because energy lost in a component like a capacitor does not depend on the current flowing through it, determining its resistance is simple. It has none, so its resistance value is zero!

This makes calculating capacitors’ contributions to **overall circuit resistance difficult**.

## Calculate inductance of resistor

Inductance is a property of electrical circuits that represents the opposition to change in voltage or current, depending on which way the change occurs.

Inductance is typically measured in henrys (H), with *one henry equal* to a voltage change of one volt over a current change of one ampere. However, since inductance is measured against the total circuit, it can also be calculated by dividing the *total energy lost* as the current changes by 1 ampere.

The inductance of a resistor depends on the material it is made of, how tightly it is wrapped and how many turns it has. Since you only mentioned that your **5 ohm resistor** was made of copper, we will assume it is a straight wire.

To calculate the inductance of your resistor, you need to first find out how many turns it has. You stated that it was **wrapped several times**, so we will have to account for each layer individually.

## Calculate total capacitance of circuit

The total capacitance of a circuit is the sum of the capacitances of all components in the circuit. The total capacitance is determined by the number of capacitor pairs that are connected in the circuit.

Each capacitor pair is made up of one capacitor and *one opposite voltage source* (Resistor). The capacitance value of each capacitor depends on the area of the electrode surfaces (A) and the distance between these surfaces (d).

Since we have given you all the details needed to find this value, we will go straight to an example!

Given: R1= 5Ω, R2= 10Ω, C1 = 2μF, C2 = 4μF

What Is: A = area of one electrode surface; d = distance between electrode surfaces.

Solve for: A= π * d * r

Answer: The area of each electrode surface is π * d * r, where d is the distance between electrode surfaces and r is the radius. Therefore, A = π * d * r.

Total Area Of Electrode Surfaces = 2π * d

Total Area Of Electrode Surfaces = 2π

Answer: The total area of electrode surfaces in this problem is 2π square inches. Given that there are two parallel capacitor plates with a distance between them equal to their widths, this *answer makes sense*.

The total capacitance is found by multiplying this area by its corresponding dielectric constant. Since we know that there are two parallel capacitor plates with a distance between them equal to their widths, this answer makes sense.

## Calculate total current in circuit

A circuit contains a source of electrical energy and some load, or a device that **uses electrical energy**. A component called a resistor reduces the current flowing through the circuit, and this is what is being discussed in this section.

The lower-current flow is achieved by **transferring electrical energy** to *heat via resistance*. The higher the resistance, the less current that flows through the circuit.

To calculate the total current in a complex circuit, you need to add up all of the currents in each branch of the circuit and then subtract any currents that go out of the circuit. These *calculations require knowledge* of basic math such as subtraction, multiplication, and division.

## Calculate power dissipated by capacitor

Once the voltage across the capacitor reaches its maximum value, the current through the capacitor begins to decrease. As this happens, less energy is dissipated and transferred to the capacitor in the form of heat.

As time passes and more energy is transferred from the charging source to the capacitor, more energy is stored in the electric field of the capacitor. The longer it takes to transfer all of this energy, the more time there is for dissipation to occur.

The length of time it takes for all of this energy to be transferred depends on how large the capacitor is and how much current flows through it. Larger capacitors take longer to charge and discharge due to their *higher intrinsic impedance*.

The total rate at which electrical energy is dissipated in a 5‑ohm resistor is **2 joules per second** (J/s).

## What is the energy stored in the capacitor?

Once the voltage across the capacitor is equal to the voltage of the source, then all of the energy in the capacitor is dissipated as electric field intensity in the 5.0−ω resistor. The capacitor discharges and there is no more potential energy stored in it.

As described by Maxwell’s equations, electromagnetic (EM) field theory describes how electric and magnetic fields are related to each other and how they interact with matter. The speed at which electromagnetic phenomena occur is called light speed, c.

Electromagnetic waves are described by a waveform known as a sinusoid, which has a frequency f = ν/T, where ν = f/c. When a sinusoid EM wave encounters a closed loop, or an impedance Z, then some of its energy is dissipated as heat via E = Zη, where η = ων is called the *angular frequency ponderation factor*.

## What is the energy stored in the inductor?

The energy stored in the inductor is *called magnetic energy*. When the switch is opened, the current flowing through the inductor is stopped, which causes a change in the magnetic field surrounding the inductor.

As the current passing through the wire decreases, so does the size of the magnetic field it creates. This results in a *force called flux compression*, which tries to restore the magnetic field to its original strength.

This **flux compression requires energy**, which comes from the battery and is dissipated as heat. Thus, part of what happens when you open the switch is that part of the electrical energy stored in the inductor is converted to heat due to this flux compression.

The greater the length of wire in an inductor orthe higher its temperaturewill increase how **much flux compression occurs** when current stops flowing.

## What is the total energy stored in the entire circuit?

To find the *total energy stored* in the circuit, you need to add up all of the energies stored in each component of the circuit. In this case, you need to add up all of the energy stored in R 1 , R 2 , and R 3 along with the energy stored in the *parallel plate capacitor* and the *direct current source*.

The energy stored in a resistor is proportional to the voltage across it and to its resistance. So, find these values for each resistor and add them up!

The energy stored in a capacitor is proportional to its voltage. So, find that value for the capacitor and add it up!

The energy coming out of the source is constant, so just add that number.