# Introduction to DC Circuits

A DC circuit is a circuit that contains:

A. a source of DC current

B. conductors that carry the current

C. an electrical device, often called a load, that is connected to the DC source via the conductors and that absorbs electrical energy from the source.

SOURCES

Every circuit has a source of electrical energy. Sources may be classified in several ways - for our purposes it is sufficient to divide sources into two groups:

DC Voltage Sources

DC Current Sources

For the most part, we will discuss ideal sources, which are defined below:

Ideal DC Voltage Source: a source of constant voltage, whose internal resistance is zero ohms that can provide any required value of current.

Ideal DC Current Source: a source of constant current, whose internal resistance is infinite that can provide any required value of voltage.

A source may be independent or dependent. An independent source is one whose value does not depend on the current or voltage present at any part of the circuit. A dependent source is one whose value depends on a voltage or current in some other part of the circuit. The symbols for the various ideal sources are shown below:

CONDUCTORS

Conductors (wires) are used to interconnect sources and loads. We will assume, unless stated otherwise that the conductors are perfect conductors that have no internal resistance.

There are many kinds of loads. We will begin by looking at the simplest possible load, a resistor. A resistor is a device that opposes the flow of electric current. Some of the energy contained in electrons flowing through the resistor is converted to heat. The amount of opposition that the resistor offers to current flow is known as its resistance, and is defined as:

R = V/I

That is, resistance of a resistor is computed by dividing the voltage across the resistor by the current flowing through it. The unit of measurement for resistance is the ohm (symbol W). The ohm is defined as the amount of resistance that produces 1 ampere of current flow when 1 volt is applied. The symbol for resistance is R

For many types of electrical devices, and most resistors, the resistance is independent of the applied voltage. In other words, a the resistance of a resistor will not change when the voltage applied to it changes. When the resistance is independent of the applied voltage, the following law holds:

V = I*R

This relationship is known as Ohm's Law, and is named after Georg Simon Ohm, the nineteenth century physicist who discovered this relationship. A resistor that follows this law is known as a linear resistor or an ideal resistor. A graph of the voltage across a resistor and the current through the resistor is shown below. Note that the current-voltage line is straight and its slope is the resistance.

Although many electrical devices follow this law, it is not universal. For a device obeying Ohm's law, a graph of voltage against current is a straight line, and the component is said to be linear or sometimes ohmic. A device designed to obey Ohm's law is referred to as a linear resistor or more usually simply as a resistor. There are other devices (e.g. diodes and transistors) which have a non-linear current-voltage relationship.

It is sometimes useful to consider the reciprocal of resistance, known as conductance, the ratio of current to voltage. Its unit is the siemens (symbol S - note distinction from lower case s for seconds). The symbol for conductance is G.

We can write Ohm's Law in several different forms. In terms of resistance:

R = V/I (definition of resistance)

V = IR  (loosely referred to as Ohm's law)

I = V/R

In terms of conductance:

G = I/V (definition of conductance)

V = I/G

I = V

Resistance and conductance are related as follows:

R = 1/G

Poor conductors or insulators tend to block the flow of current and have a high resistance or low conductance. Good conductors offer little opposition to current flow and have a low resistance or a high conductance.

Now let's work some examples.

Example 1: We measure the voltage across a resistor and find it to be 17 V. We measure the current through the resistor and find that it is 0.4 A. What is the resistance of the resistor?

Solution:

Since we know voltage and current, we use the following form of Ohm's Law

R = V/I.

Putting in the values for voltage and current gives:

R = 17/0.4 = 42.5 ohms

Example 2. We apply 240 V to a 22,000 ohm resistor. What is the current that flows through the resistor?

Solution:

We want to determine the current, so we use the following form of Ohm's Law:

I = V/R

Putting in values for V and R gives:

I = 240/22,000 =  0.0109 A.

When the value of the current is small (much less than 1 A) we use a smaller unit of current, the milliampere (symbol mA). One thousand  milliamperes = 1 ampere, or:

1000mA = 1 A.

The answer to this example, expressed in mA is 10.9 mA. We can convert a current in A to a current in mA by multiplying by 1000.

Example 3: A resistor of resistance 68 KW is connected to a power supply. The current through the resistor is 0.01 A, or 10 mA. What is the power supply voltage?

Solution:

First, we must know what "KW" is. The "KW" stands for kiloohm. 1 KW = 1000 ohms. Our resistor has a resistance of 68KW which is also 68,000 ohms. Now we can apply Ohm's Law:

V = IR = (0.01A)*(68,000 ohms) = 680 V

Very large resistors have resistance measured in MW. 1MW = 1000KW   = 1,000,000W

When we are speaking about the values of resistors, KW   is usually pronounced "kay" and MW   is pronounced "meg".

Example 4:  The voltage measured across a 500 foot long piece of copper wire is 1.2 V. The current flowing through the wire is 150 A. What is the conductance of the wire?

Solution:

We know that conductance is defined by the following equation:

G = I/V

Putting the measured values into the equation gives:

G = 150/1.2 = 125 S.

The symbol for the unit is  Siemens, abbreviated with a capital "S" to differentiate it from seconds, which are abbreviated with a lower case "s". Notice that the conductivity is quite large, which is what one would expect for a copper wire.

Sometimes it is hard to know which form of Ohm's Law to use. The pie chart below may be helpful

To use this chart, cover up the value (V, I or R) that you would like to find. The position of the remaining two values gives you the right form of Ohm's Law to use. Here is an example:

Example 5: We wish to determine voltage. What form of Ohm's Law should we use?

Solution:

Cover up the part of the pie containing the "V". Here is what is left:

Therefore V = IR.

Another example:

Example 6: What form of Ohm's Law can be used to find the current?

Solution:

Black out the part of the pie containing "I". You are left with:

Therefore, I = V/R

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