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DC Circuits

DC Circuit Theory

All materials are made up from atoms, and all atoms consist of protons, neutrons and electrons. Protons have a positive electrical charge, neutrons have no electrical charge, while electrons have a negative electrical charge. Atoms are bound together by powerful forces of attraction existing between the atoms nucleus and the electrons in its outer shell.
When these protons, neutrons and electrons are together within the atom they are stable. But if we separate them from each other, they want to reform and start to exert a potential of attraction called a potential difference. Now if we create a closed circuit these loose electrons will start to move and drift back to the protons due to their attraction creating a flow of electrons. This flow of electrons is called an electrical current. The electrons do not flow freely through the circuit as the material they move through creates a restriction to the electron flow. This restriction is called resistance.

Electrical Voltage

In DC circuit theory, voltage (V) is the potential energy of an electrical supply stored in the form of an electrical charge. Voltage can be thought of as the force that pushes electrons through a conductor and the greater the voltage the greater is its ability to “push” the electrons through a given circuit. The difference in voltage between any two points, connections or junctions (called nodes) in a circuit is known as the Potential Difference (p.d.) commonly called the Voltage Drop.

A voltage source that is unchanging and constant over time is called a DC voltage, while a voltage source that varies periodically in amplitude over time is called an AC voltage.
Batteries, power supplies or solar cells produce a D.C. (direct current) voltage source of a fixed value and polarity. A.C. (alternating current) voltage sources on the other hand such as those available for homes, offices and industrial applications have a value relating to the power they supply. The voltage and frequency of mains alternating current (AC) electricity used in homes is typically 230 volts AC (230V) in Europe and 110 volts AC (110V) in the USA.
General electronic circuits operate on low voltage DC battery supplies of between 1.5V and 24V dc.

Voltage is always measured as the difference between any two points in a circuit and the voltage between these two points is generally referred to as the Voltage Drop.
Voltage can exist across a circuit without current, but current cannot exist without voltage.

Electrical Current

In DC circuit theory, electrical Current (I) is the movement or flow of electrical charge and is measured in Amperes. It is the continuous and uniform flow (called a drift) of electrons (the negative particles of an atom) around a circuit that are being “pushed” by the voltage source.
Conventional Current Flow gives the flow of electrical current from positive to negative and which is the opposite in direction to the actual flow of electrons. The flow of electrons around the circuit is opposite to the direction of the conventional current flow being negative to positive. The actual current flowing in an electrical circuit is composed of electrons that flow from the negative pole of the battery (the cathode) and return back to the positive pole (the anode) of the battery.
This is because the charge on an electron is negative by definition and so is attracted to the positive terminal. This flow of electrons is called Electron Current Flow.

Current that flows in a single direction is called “Direct Current”, or D.C. Electric current that alternates back and forth through the circuit is known as “Alternating Current”, or A.C..

Resistance

Resistance (R) is the capacity of a material to resist or prevent the flow of current, the flow of electric charge within a circuit. The circuit element which does this is called the Resistor. Low resistance, for example 1Ω or less implies that the circuit is a good conductor made from materials such as copper, aluminium or carbon while a high resistance, 1MΩ or more implies the circuit is a bad conductor made from insulating materials such as glass, porcelain or plastic.

A “semiconductor” on the other hand such as silicon or germanium, is a material whose resistance is half way between that of a good conductor and a good insulator.

Resistance can be linear or non-linear in nature, but never negative. Linear resistance obeys Ohm’s Law as the voltage across the resistor is linearly proportional to the current through it. Non-linear resistance, does not obey Ohm’s Law but has a voltage drop across it that is proportional to some power of the current.
For very low values of resistance, for example milli-ohms, (mΩ) it is sometimes much easier to use the reciprocal of resistance (1/R) rather than resistance (R) itself. The reciprocal of resistance is called Conductance, symbol (G) and represents the ability of a conductor or device to conduct electricity.

Resistor is an electrical component, while resistance is the slope of the straight line defined by Ohm’s law and as such resistance is always positive, and never negative.

Then, all basic electrical or electronic circuits consist of three separate but very much related electrical quantities: Voltage, Current and Resistance; V = I x R, Ohm's Law.

Any Electrical device or component that obeys “Ohms Law” that is, the current flowing through it is proportional to the voltage across it ( I ∝ V ), such as resistors or cables, are said to be “Ohmic” in nature, and devices that do not, such as transistors or diodes, are said to be “Non-ohmic” devices.

Electrical Power (P) in a circuit is the rate at which electrical energy is absorbed or produced within a circuit. A source of energy such as a voltage will produce or deliver power while the connected load absorbs it, P = V x I.
Electrical devices convert one form of power into another. So for example, an electrical motor will convert electrical energy into a mechanical force, while an electrical generator converts mechanical force into electrical energy. A light bulb converts electrical energy into both light and heat. Power within an electrical circuit is only present when BOTH voltage and current are present, so not for open-circuit condition or short-circuit condition.

Electrical Energy is the capacity to do work, and the unit of work or energy is the joule (J). Electrical energy is the product of power multiplied by the length of time it was consumed. So if we know how much power, in Watts is being consumed and the time, in seconds for which it is used, we can find the total energy used in watt-seconds; Electrical Energy = Power, (W) x Time, (s).
Electrical energy is defined as being watts per second or joules. Although electrical energy is measured in Joules it can become a very large value when used to calculate the energy consumed by a component. For example, if a 100 watt light bulb is left “ON” for 24 hours, the energy consumed will be 8,640,000 Joules (100W x 86,400 seconds), so prefixes such as kilojoules (kJ = 10³J) or megajoules (MJ = 10⁶J) are used instead and in this simple example, the energy consumed will be 8.64MJ (mega-joules). If the electrical power consumed (or generated) is measured in watts or kilowatts (thousands of watts) and the time is measure in hours not seconds, then the unit of electrical energy will be the kilowatt-hours, (kWhr). Then our 100 watt light bulb will consume 2,400 watt hours or 2.4kWhr, which is much easier to understand the 8,640,000 joules.

θ – Phase Angle, The Phase Angle is the difference in degrees between the voltage waveform and the current waveform having the same periodic time. It is a time difference or time shift and depending upon the circuit element can have a “leading” or “lagging” value. The phase angle of a waveform is measured in degrees or radians.

Sometimes in complex circuits, we can not simply use Ohm’s Law alone to find the voltages or currents circulating within the circuit. For these types of calculations we need certain rules which allow us to obtain the circuit equations and for this we can use Kirchhoffs Circuit Laws. In 1845, a German physicist, Gustav Kirchhoff developed a pair or set of rules or laws which deal with the conservation of current and energy within electrical circuits. These two rules are commonly known as Kirchhoffs Circuit Laws with one of Kirchhoffs laws dealing with the current flowing around a closed circuit, Kirchhoffs Current Law, (KCL) while the other law deals with the voltage sources present in a closed circuit, Kirchhoffs Voltage Law, (KVL).

Common DC Circuit Theory Terms

· Circuit – a circuit is a closed loop conducting path in which an electrical current flows.
· Path – a single line of connecting elements or sources.
· Node – a node is a junction, connection or terminal within a circuit were two or more circuit elements are connected or joined together giving a connection point between two or more branches. A node is indicated by a dot.
· Branch – a branch is a single or group of components such as resistors or a source which are connected between two nodes.
· Loop – a loop is a simple closed path in a circuit in which no circuit element or node is encountered more than once.
· Mesh – a mesh is a single closed loop series path that does not contain any other paths. There are no loops inside a mesh.