The purpose of electronic circuits is to control the flow of electric currents. This may sound like a silly question, but why do we need to control the currents? Well, it has been found experimentally that the intensity of various electrical effects is related to the amount of the charge Q that passes by a certain region per unit time. By controlling this amount we can vary the intensity of these effects. That's why this quantity I=Q/t, which is called the current, presents a special interest in engineering.

In practice, the flow of the current can be controlled by various electronic components. A network of interconnected components that can accomplish a certain task is referred to as electronic circuit. Such networks can be used for processing signals, information, or energy. For the charges to flow continuously, the circuit should have an energy source and a closed path.

Let's see how the moving charge relates to electric power. When a charged particle is placed in an electrical field, it experiences a force that depends on its position. Such particle therefore has a potential energy associated with this position. When it moves from one point to another, the amount of work done by the field equals the drop in partical's energy, which is being converted into other energy forms, such as mechanical motion, heat and light. The change in the potential energy of a particle per unit charge as it moves from one point to another is defined as voltage or potential difference between these two points: V=ΔE/q. The power transfer is then equals to: P=ΔE/t=Vq/t=VI. Note that only voltage differences rather than absolute voltages have direct physical meaning. The voltage between two points can be measured by an instrument called a voltmeter and the current can be measured by an ammeter. A voltmeter can be just an ammeter with a series-connected high-value resistor through which the current proportional to the measured voltage is forced to flow. For hobbyist electronic projects there are inexpensive digital multimeters that can measure voltage, current, and resistance.

Series and parallel connections


Impedance by definition is the ratio of the voltage to the current. Components in a circuit can be connected in series or in parallel (see diagram to the right). With series connection, the same current flows through all elements and impedances add up. With parallel connection the same voltage is applied to all elements and conductances add up. In both cases the location of any element in the chain does not matter: see equations for both types of connections. In a purely resistive component the relationship between V and i is determined by its resistance according to Ohm's law. The V/i relationships for energy storage components (inductors and capacitors) are generally described by differential equations. In large circuits the handling of these equations quickly becomes practically unmanageable. That's why the analysis of the networks with sinusoidal signals usually uses complex exponentials method.
With this method, voltages and currents are represented by complex functions (phasors) based on Euler relationship ejx=cosx+jsinx, where j is imaginary unit. Complex numbers basically represent two variables as a single quantity. The lenght of the phasor is proportional to the magnitude of the quantity it represents, and its angle represents a phase shift relative to some reference signal. This allows turning differential equations into algebraic equations. In linear AC networks with single-frequency sinusoidal voltage sources we can introduce so-called complex impedance Z defined as the ratio of voltage phasor to the current phasor: Z=V/Ĩ. Its magnitude is the ratio of the voltage amplitude to the current amplitude, and phase is the phase shift between the current and the voltage. The introduction of complex impedance allows us to extend Ohm's law to reactive (non-resistive) components.

Ohm's law pie chart


Impedance in general can be presented as a complex number that can be calculated by using formulas for series and parallel connections. With known Z, current phasor is Ĩ=V/Z. This pie chart ("wheel") modified for AC circuits illustrates relationships between various quantities in linear networks with a sinusoidal input. These formulas are adaptations of Ohm's law and Joule's law for AC signals. In this "power wheel":
V - rms voltage (volts);
I - rms current (amps);
Z - magnitude of impedance (ohms);
S - apparent power (volt-amps).
By knowing any two values of V, I, Z or S, you can find the values of the remaining quantities.
For a pure resistor Z=R, I=V/R, and S=P, where R - resistance, P - active power.

To use this Ohm's law calculator enter any two values and select "Calculate". This tool will display the remaining values. For I-V relationships between basic electrical parts see electrical formulas.


Every circuit design starts with the development of a schematic. A schematic diagram is a drawing where components are represented by graphical symbols and that can communicate information about a circuit. In theory, the processes in electronic circuits could be described by Maxwell's equations and the physics laws describing properties of materials. However, in practical design and analysis, engineers consider idealized elements that reflect some essential aspects of the operation of the real devices. This allows describing the operation of the circuit with simplified equations that use circuit theory terms.

The basis for circuit analysis technique are Kirchoff's current and voltage laws in conjunction with Ohm's law extended for AC. There are also a number of network theorems and methods (such as Thevenin, Norton, Superposition, Y-Delta transform) that are derived from these three laws.

The circuit design typically includes computer simulation, breadboarding and prototyping.

Electronic devices are normally assembled on printed circuit boards (PCBs) that mechanically support and electrically interconnect parts by using conductive traces, etched from copper sheets laminated onto an isolating substrate. The size of the traces is calculated based on their current-carrying capacity and acceptable impedance.


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