# Circuit Elements And Sources

This chapter provides an overview of most commonly used **elements in electric circuits**. It also contains laws governing the current through and voltage across these components as well as the power supplied/dissipated and energy storage in this context. In addition, difference between ideal and nonideal voltage and current sources is highlighted including a discussion on sign convention i.e. voltage polarity and current direction.

The concepts of current and voltage are first introduced as these constitutes one of the most fundamental concepts particularly in electronics and electrical engineering.

## Current

Current can be defined as the motion of charge through a conducting material. The unit of current is Ampere whilst charge is measured in Coulombs.

### Definition of an Ampere

*“The quantity of total charge that passes through an arbitrary cross section of a conducting material per unit second is defined as an Ampere.”*

### Mathematically,

where Q is the symbol of charge measured in Coulombs (C), I is the current in amperes (A) and t is the time in seconds (s). The current can also be defined as the rate of charge passing through a point in an electric circuit i.e.

A constant current (also known as direct current or DC) is denoted by the symbol I whereas a timevarying current (also known as alternating current or AC) is represented by the symbol i or i(t).

Current is always measured through a circuit element.

In the figure below demonstrates the use of an ampere-meter or ammeter in series with a circuit element, R, to measure the current through it.

An ammeter is connected in series to measure current, I, through the element, R.

### Voltage or Potential Difference

Definition

*Voltage or potential difference between two points in an electric circuit is 1 V if 1 J (Joule) of energy is expended in transferring 1 C of charge between those points.*

It is generally represented by the symbol V and measured in volts (V). Note that the symbol and the unit of voltage are both denoted by the same letter, however, it rarely causes any confusion.

The symbol V also signifies a constant voltage (DC) whereas a time-varying (AC) voltage is represented by the symbol v or v(t).

*Voltage is always measured across a circuit element as demonstrated in figure below.*

A voltmeter is connected in parallel with the circuit element, R to measure the voltage across it

A voltage source provides the energy or emf (electromotive force) required for current flow. However, current can only exist if there is a potential difference and a physical path to flow. A potential difference of V between two points implies 0 A of current flowing through them. The current I in the figure below is 0 A since the potential difference across R2 is 0 V. In this case, a physical path exists but there is no potential difference. This is equivalent to an open circuit.

The potential difference across R2 is 0 V, hence the current I is 0 A where Vs and Is are the voltage and current sources respectively.