Basic Concepts of DC Circuits

Introduction

An electric circuit is an interconnection of electrical elements.

Systems of Units

Charge

The most basic quantity in an electric circuit is the electric charge.

Charge is an electrical property of the atomic particles of which matter consists, measured in coulombs (C).

The charge e on an electron is -1.602 x 10-19 C.

Charge (cont.)

Current

A unique feature of electric charge or electricity is that it is mobile; it can be transferred where it can be converted to another form of energy.

When a conducting wire is connected to a battery, the charges are compelled to move; positive charges in one direction and negative charges in the opposite direction.

Current (cont.)

This motion of charges is what creates an electrical current.

Electric current is the time rate of change of charge, measured in amperes (A).

1 ampere = 1 coulomb / second It is conventional to take the current flow

as the movement of positive charges, although current is actually due to negatively charged electrons.

Current (cont.)

A direct current (dc) is a current that remains constant with time.

An alternating current (ac) is a current that varies sinusoidally with time.

The Relationship

Mathematically, the relationship between current i, charge q, and time t is

The charge transferred between time t0 and t is found by integrating both sides;

Voltage

To move an electron in a particular direction requires some work or energy transfer. This work is performed by an external electromotive force (emf), typically a battery.

This emf is also known as potential difference or voltage.

Voltage (cont.)

The voltage between two points a and b is the energy (or work) needed to move a unit charge from a to b.

where w is energy in joules (J) and q is charge (C). The voltage is measured in volts (V).

1 volt = 1 joule / coulomb = 1 newton*meter/ coulomb

Voltage Polarity

The plus (+) and minus (-) signs are used to define reference direction or voltage polarity.

vab = -vba

The polarity can be interpreted in two ways:

Power

Although current and voltage are the two basic variables, they are not sufficient by themselves.

For practical purposes, we need to know how much power a device can handle and how much energy is consumed over a period of time.

Power (cont.)

To relate power and energy to voltage and current, we recall that:

power is the time rate of expending or absorbing energy, measured in watts (W).

We write this relationship as

p is power in watts (W), w is energy in joules (J) and t is time in seconds (s).

Power (cont.)

The power p is a time-varying quantity and is called instantaneous power.

p > 0, power is absorbed p < 0, power is supplied power absorbed = - power supplied

Power (cont.)

The law of conservation of energy must be obeyed in any circuit. For with this reason, the sum of power in a circuit must be zero.

Energy

Energy is the capacity to do work, measured in joules (J).

The energy absorbed or supplied by an element from time t0 to t is

Circuit Elements

An element is a basic building block of a circuit.

There are two types of elements: active and passive.

Circuit Elements (cont.)

Active elements are capable of generating energy

Generators Batteries Amplifiers

Passive elements cannot create energy

Resistors Capacitors Inductors

Circuit Elements (cont.)

The most important active elements are voltage and current sources because they deliver power to the circuit.

There are two types of sources: independent and dependent.

Circuit Elements (cont.)

Independent sources provide a specified voltage or current that is completely independent of other circuit variables.

Dependent sources have their source quantity controlled by another voltage or current.

Circuit Elements (cont.)

There are 4 possible types of dependent sources: voltage controlled voltage source, current controlled voltage source, voltage controlled current source, and current controlled current source.