## Different Types of Currents

An electrical circuit is an interconnection of electrical elements that has a closed loop giving a return path for the current.

### LEARNING OBJECTIVES

Describe structure of an electrical circuit and identify elements of a direct current circuit

### KEY TAKEAWAYS

#### Key Points

- Direct current ( DC ) is the unidirectional flow of electric charge. Direct current is produced by sources such as batteries, thermocouples, solar cells, and commutator-type electric machines of the dynamo type.
- A direct current circuit is an electrical circuit that consists of constant voltage sources, constant current sources, and resistors. It is common to refer to a circuit that is powered by a DC voltage source as a DC circuit even though what is meant is that the circuit is DC powered.
- A number of electrical laws apply to all electrical networks: Ohm ‘s law, Kirchhoff’s current and voltage laws, Norton’s theorem, and Thévenin’s theorem. With these, it is possible to calculate the electric potential and current at each point in the circuit.

#### Key Terms

**current-voltage characteristic**: A current–voltage characteristic or I–V curve (current–voltage curve) is a relationship between the electric current through a circuit, device, or material, and the corresponding voltage, or potential difference across it.**electrical circuit**: An interconnection of electrical elements such as resistors, inductors, capacitors, transmission lines, voltage sources, current sources and switches that has a closed loop giving a return path for the current.**direct current**: An electric current in which the electrons flow in one direction, but may vary with time.

### Overview

An electrical network is an interconnection of electrical elements such as resistors, inductors, capacitors, transmission lines, voltage sources, current sources and switches. An electrical circuit is a special type of network, one that has a closed loop giving a return path for the current. Electrical networks that consist only of sources (voltage or current), linear lumped elements (resistors, capacitors, inductors), and linear distributed elements (transmission lines) can be analyzed by algebraic and transform methods. A resistive circuit is a circuit containing only resistors and ideal current and voltage sources. Analysis of resistive circuits is less complicated than analysis of circuits containing capacitors and inductors. If the sources are constant (DC) sources, the result is a DC circuit. A network that contains active electronic components is known as an electronic circuit. Such networks are generally nonlinear and require more complex design and analysis tools.

### Direct Current Circuits

Direct current (DC) is the unidirectional flow of electric charge. Direct current is produced by sources such as batteries, thermocouples, solar cells, and commutator-type electric machines of the dynamo type. Direct current may flow in a conductor such as a wire, but can also flow through semiconductors, insulators, or even through a vacuum as in electron or ion beams. The electric charge flows in a constant direction, distinguishing it from alternating current (AC). A term formerly used for direct current was galvanic current.

A direct current circuit is an electrical circuit that consists of any combination of constant voltage sources, constant current sources, and resistors. In this case, the circuit voltages and currents are independent of time. A particular circuit voltage or current does not depend on the past value of any circuit voltage or current. This implies that the system of equations that represent a DC circuit do not involve integrals or derivatives with respect to time. If a capacitor or inductor is added to a DC circuit, the resulting circuit is not, strictly speaking, a DC circuit. However, most such circuits have a DC solution. This solution gives the circuit voltages and currents when the circuit is in DC steady state. Such a circuit is represented by a system of differential equations. The solution to these equations usually contain a time varying or transient part as well as constant or steady state part. It is this steady state part that is the DC solution. In electronics, it is common to refer to a circuit that is powered by a DC voltage source such as a battery or the output of a DC power supply as a DC circuit even though what is meant is that the circuit is DC powered.

A simple DC circuit is illustrated in. In circuit diagrams such as this, electrical elements are represented by symbols and usually labeled with appropriate characteristics, such as the resistance *r* of a resistor. The electric potential and current may also be labeled at various points of the circuit. However, please be aware that circuit diagram conventions do differ among textbooks and subject fields, leading to different symbols being used for the same circuit elements.

### Physical Laws Related to Circuit Analysis

A number of electrical laws apply to all electrical networks. These include Ohm’s law, which has been discussed in the “Resistance and Resistors” module, Kirchhoff’s current and voltage laws, which are covered in the “Kirchhoff’s Rules” module. The two Kirchoff laws along with the current-voltage characteristic (I-V curve) of each electrical element completely describe a circuit. With these, it is possible to calculate the electric potential and current at each point in the circuit. In addition, Norton’s theorem and Thévenin’s theorem are useful in analyzing complicated circuits.

## Sources of EMF

Electromotive force (EMF) is the voltage voltage generated by a battery or by the magnetic force according to Faraday’s Law of Induction.

### LEARNING OBJECTIVES

Give examples of the devices that can provide the electromotive force

### KEY TAKEAWAYS

#### Key Points

- EMF is classified as the external work expended per unit of charge to produce an electric potential difference across two open-circuited terminals.
- Devices that can provide EMF include electrochemical cells, thermoelectric devices, solar cells, electrical generators, transformers, and even Van de Graaff generators.
- In nature, EMF is generated whenever magnetic field fluctuations occur through a surface.

#### Key Terms

**battery**: A device that produces electricity by a chemical reaction between two substances.**electromotive force**: (EMF)—The voltage generated by a battery or by the magnetic force according to Faraday’s Law. It is measured in units of volts, not newtons, and thus, is not actually a force.**Faraday’s law of induction**: Is a basic law of electromagnetism that predicts how a magnetic field will interact with an electric circuit to produce an electromotive force.

### Electromotive Force

Electromotive force, also called EMF (denoted and measured in volts) refers to voltage generated by a battery or by the magnetic force according to Faraday’s Law of Induction, which states that a time varying magnetic field will induce an electric current.

Electromotive “force” is not considered a force (as force is measured in newtons) but a potential, or energy per unit of charge, measured in volts. Formally, EMF is classified as the external work expended per unit of charge to produce an electric potential difference across two open-circuited terminals. By separating positive and negative charges, electric potential difference is produced, generating an electric field. The created electrical potential difference drives current flow if a circuit is attached to the source of EMF. When current flows, however, the voltage across the terminals of the source of EMF is no longer the open-circuit value, due to voltage drops inside the device due to its internal resistance.

Devices that can provide EMF include electrochemical cells (batteries), thermoelectric devices, solar cells, electrical generators, transformers, and even Van de Graaff generators (examples shown in ).

In the case of a battery, charge separation that gives rise to a voltage difference is accomplished by chemical reactions at the electrodes; voltaic cells can be thought of as having a “charge pump” of atomic dimensions at each electrode.

In the case of an electrical generator, a time-varying magnetic field inside the generator creates an electric field via electromagnetic induction, which in turn creates an energy difference between generator terminals. Charge separation takes place within the generator, with electrons flowing away from one terminal and toward the other, until, in the open-circuit case, sufficient electric field builds up to make further movement unfavorable. Again the EMF is countered by the electrical voltage due to charge separation. If a load is attached, this voltage can drive a current. The general principle governing the EMF in such electrical machines is Faraday’s law of Induction.

In nature, EMF is generated whenever magnetic field fluctuations occur through a surface. An example of this is the varying Earth magnetic field during a geomagnetic storm, acting on anything on the surface of the planet, like an extended electrical grid.

## Resistors in Series and Parallel

## Resistors in Series

The total resistance in the circuit with resistors connected in series is equal to the sum of the individual resistances.

### LEARNING OBJECTIVES

Calculate the total resistance in the circuit with resistors connected in series

### KEY TAKEAWAYS

#### Key Points

- The same current flows through each resistor in series.
- Individual resistors in series do not get the total source voltage, but divide it.
- The total resistance in a series circuit is equal to the sum of the individual resistances:

$\text{RN}(\text{series})={\text{R}}_{1}+{\text{R}}_{2}+{\text{R}}_{3}+\dots +{\text{R}}_{\text{N}}$.

#### Key Terms

**series**: A number of things that follow on one after the other or are connected one after the other.**resistance**: The opposition to the passage of an electric current through that element.

### Overview

Most circuits have more than one component, called a resistor, that limits the flow of charge in the circuit. A measure of this limit on charge flow is called resistance. The simplest combinations of resistors are the series and parallel connections. The total resistance of a combination of resistors depends on both their individual values and how they are connected.

### Resistors in Series

Resistors are in series whenever the flow of charge, or the current, must flow through components sequentially.

shows resistors in series connected to a voltage source. The total resistance in the circuit is equal to the sum of the individual resistances, since the current has to pass through each resistor in sequence through the circuit.

### Using Ohm ‘s Law to Calculate Voltage Changes in Resistors in Series

According to Ohm’s law, the voltage drop, V, across a resistor when a current flows through it is calculated by using the equation V=IR, where I is current in amps (A) and R is the resistance in ohms (Ω).

So the voltage drop across R_{1} is V_{1}=IR_{1}, across R_{2} is V_{2}=IR_{2}, and across R_{3} is V_{3}=IR_{3}. The sum of the voltages would equal: V=V_{1}+V_{2}+V_{3}, based on the conservation of energy and charge. If we substitute the values for individual voltages, we get:

$\text{V}={\text{IR}}_{1}+{\text{IR}}_{2}+{\text{IR}}_{3}$

or

$\text{V}=\text{I}({\text{R}}_{1}+{\text{R}}_{2}+{\text{R}}_{3})$

This implies that the total resistance in a series is equal to the sum of the individual resistances. Therefore, for every circuit with *N* number of resistors connected in series:

$\text{RN}(\text{series})={\text{R}}_{1}+{\text{R}}_{2}+{\text{R}}_{3}+\dots +{\text{R}}_{\text{N}}.$

Since all of the current must pass through each resistor, it experiences the resistance of each, and resistances in series simply add up.

Since voltage and resistance have an inverse relationship, individual resistors in series do not get the total source voltage, but divide it. This is indicated in an example of when two light bulbs are connected together in a series circuit with a battery. In a simple circuit consisting of one 1.5V battery and one light bulb, the light bulb would have a voltage drop of 1.5V across it. If two lightbulbs were connected in series with the same battery, however, they would each have 1.5V/2, or 0.75V drop across them. This would be evident in the brightness of the lights: each of the two light bulbs connected in series would be half as dim as the single light bulb. Therefore, resistors connected in series use up the same amount of energy as a single resistor, but that energy is divided up between the resistors depending on their resistances.

## Resistors in Parallel

The total resistance in a parallel circuit is equal to the sum of the inverse of each individual resistances.

### LEARNING OBJECTIVES

Calculate the total resistance in the circuit with resistors connected in parallel

### KEY TAKEAWAYS

#### Key Points

- The total resistance in a parallel circuit is less than the smallest of the individual resistances.
- Each resistor in parallel has the same voltage of the source applied to it (voltage is constant in a parallel circuit).
- Parallel resistors do not each get the total current; they divide it (current is dependent on the value of each resistor and the number of total resistors in a circuit).

#### Key Terms

**resistance**: The opposition to the passage of an electric current through that element.**parallel**: An arrangement of electrical components such that a current flows along two or more paths.

### Overview

Resistors in a circuit can be connected in series or in parallel. The total resistance of a combination of resistors depends on both their individual values and how they are connected.

### Resistors in Parallel

Resistors are in parallel when each resistor is connected directly to the voltage source by connecting wires having negligible resistance. Each resistor thus has the full voltage of the source applied to it.

Each resistor draws the same current it would if it were the only resistor connected to the voltage source. This is true of the circuitry in a house or apartment. Each outlet that is connected to a appliance (the “resistor”) can operate independently, and the current does not have to pass through each appliance sequentially.

### Ohm ‘s Law and Parallel Resistors

Each resistor in the circuit has the full voltage. According to Ohm’s law, the currents flowing through the individual resistors are

${\text{I}}_{1}=\frac{\text{V}}{{\text{R}}_{1}}$,

${\text{I}}_{2}=\frac{\text{V}}{{\text{R}}_{2}}$, and

${\text{I}}_{3}=\frac{\text{V}}{{\text{R}}_{3}}$. Conservation of charge implies that the total current is the sum of these currents:

$\text{I}={\text{I}}_{1}+{\text{I}}_{2}+{\text{I}}_{3}.$

Substituting the expressions for individual currents gives:

$\text{I}=\frac{\text{V}}{{\text{R}}_{1}}+\frac{\text{V}}{{\text{R}}_{2}}+\frac{\text{V}}{{\text{R}}_{3}}$

or

$\text{I}=\text{V}(\frac{1}{{\text{R}}_{1}}+\frac{1}{{\text{R}}_{2}}+\frac{1}{{\text{R}}_{3}})$

This implies that the total resistance in a parallel circuit is equal to the sum of the inverse of each individual resistances. Therefore, for every circuit with

$\text{n}$number or resistors connected in parallel,

${\text{R}}_{\text{n}\phantom{\rule{thickmathspace}{0ex}}(\text{parallel})}=\frac{1}{{\text{R}}_{1}}+\frac{1}{{\text{R}}_{2}}+\frac{1}{{\text{R}}_{3}}\dots +\frac{1}{{\text{R}}_{\text{n}}}.$

This relationship results in a total resistance that is less than the smallest of the individual resistances. When resistors are connected in parallel, more current flows from the source than would flow for any of them individually, so the total resistance is lower.

Each resistor in parallel has the same full voltage of the source applied to it, but divide the total current amongst them. This is exemplified by connecting two light bulbs in a parallel circuit with a 1.5V battery. In a series circuit, the two light bulbs would be half as dim when connected to a single battery source. However, if the two light bulbs were connected in parallel, they would be equally as bright as if they were connected individually to the battery. Because the same full voltage is being applied to both light bulbs, the battery would also die more quickly, since it is essentially supplying full energy to both light bulbs. In a series circuit, the battery would last just as long as it would with a single light bulb, only the brightness is then divided amongst the bulbs.