UNIT 1

Basic Electrical Terms and Units

Electrical voltage:

Electrical voltage is defined as electric potential difference between two points of an electric field.

V = φ2 - φ1

V is the voltage between point 2 and 1 in volts (V).

φ2 is the electric potential at point 2 in volts (V).

φ1 is the electric potential at point 1 in volts (V).

Electrical current:

Electrical current is the flow rate of electrical charge in electric field, usually in electrical circuit.

Electrical current is measured by the rate of electric charge flow in an electrical circuit:

i(t) = dQ(t) / dt

The momentary current is given by the derivative of the electric charge by time.

i(t) is the momentary current I at time t in amps (A).

Q(t) is the momentary electric charge in coulombs (C).

t is the time in seconds (s).

Resistance:

Resistance is an electrical quantity that measures how the device or material reduces the electric current flow through it.

The resistance is measured in units of ohms (Ω).

The resistance of a conductor is resistivity of the conductor's material times the conductor's length divided by the conductor's cross -sectional area.

R = x l/A

R is the resistance in ohms (Ω).

ρ is the resistivity in ohms-meter (Ω×m)

l is the length of the conductor in meter (m)

A is the cross -sectional area of the conductor in square meters (m2)

Electric power

The electric power P is equal to the energy consumption E divided by the consumption time t:

P = E/t

P is the electric power in watt (W).

E is the energy consumption in joule (J).

t is the time in seconds (s).

Example

Find the electric power of an electrical circuit that consumes 120 joules for 20 seconds.

Solution:

E = 120J

t = 20s

P = E / t = 120J / 20s = 6W

Electric charge:

Electric charge generates electric field.

The electric charge influence other electric charges with electric force and get influenced by the other charges with the same force in the opposite direction.

There are 2 types of electric charge:

#### Positive charge (+)

Positive charge has more protons than electrons (Np>Ne).

Positive charge is denoted with plus (+) sign.

The positive charge attracts other negative charges and repels other positive charges.

The positive charge is attracted by other negative charges and repelled by other positive charges.

#### Negative charge (-)

Negative charge has more electrons than protons (Ne>Np).

Negative charge is denoted with minus (-) sign.

Negative charge attracts other positive charges and repels other negative charges.

The negative charge is attracted by other positive charges and repelled by other negative charges.

The electric charge is measured with the unit of Coulomb [C].

One coulomb has the charge of 6.242×1018 electrons:

1C = 6.242×1018 e

Power efficiency is defined as the ratio of the output power divided by the input power:

η = 100% ⋅ Pout / Pin

η is the efficiency in percent (%).

Pin is the input power consumption in watts (W).

Pout is the output power or actual work in watts (W).

Alternating Current (AC) — An electric current that reverses its direction many times a second at regular intervals.

Capacitance — The ability of a body to store an electrical charge. Measured in farads as the ratio of the electric charge of the object (Q, measured in coulombs) to the voltage across the object (V, measured in volts).

Capacitor — A device used to store an electric charge, consisting of one or more pairs of conductors separated by an insulator. Commonly used for filtering out voltage spikes.

Circuit — A closed path in which electrons from a voltage or current source flow. Circuits can be in series, parallel, or in any combination of the two.

Conductor — Any material where electric current can flow freely. Conductive materials, such as metals, have a relatively low resistance. Copper and aluminum wire are the most common conductors.

Current (I) — The flow of an electric charge through a conductor. An electric current can be compared to the flow of water in a pipe. Measured in amperes.

Diode — A semiconductor device with two terminals, typically allowing the flow of current in one direction only. Diodes allow current to flow when the anode is positive in relation to the cathode.

Direct Current (DC) — An electric current that flows in only one direction.

Electromotive Force — (EMF) A difference in potential that tends to give rise to an electric current. Measured in volts.

Electron — A tiny particle which rotates around the nucleus of an atom. It has a negative charge of electricity.

Ohm’s law states that the voltage or potential difference between two points is directly proportional to the current or electricity passing through the resistance, and directly proportional to the resistance of the circuit.

The formula for Ohm’s law is

V=IR-----------------------------------------------------------(1)

This relationship between current, voltage, and relationship was discovered by German scientist Georg Simon Ohm.

Ohm’s law states that the current through a conductor between two points is directly proportional to the voltage across the two points.

Resistor and its coding

Resistor colour coding uses coloured bands to quickly identify a resistors resistive value and its percentage of tolerance with the physical size of the resistor indicating its wattage rating.

The colours brown, red, green, blue, and violet are used as tolerance codes on 5-band resistors only. All 5-band resistors use a coloured tolerance band.

The blank (20%) “band” is only used with the “4-band” code (3 coloured bands + a blank “band”).

Yellow-Violet-Orange-Gold Colour Code

A resistor coloured Yellow-Violet-Orange-Gold would be 47 kΩ with a tolerance of +/- 5%.

Green-Red-Gold-Silver Colour Code

A resistor coloured Green-Red-Gold-Silver would be 5.2 Ω with a tolerance of +/- 10%.

Properties:

- The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area.
- Resistance also depends on the material of the conductor.
- The resistance of a conductor, or circuit element, generally increases with increasing temperature.
- The reciprocal of the resistance, 1/R, is called the conductance and is expressed in units of reciprocal ohm, called mho.
- Electric noise appears in every resistor and is for low-noise amplifying applications of importance. For high frequency applications, the inductance and capacitance properties play a role.

Temperature co-efficient of resistance:

Temperature coefficient of resistance is the measure of change in electrical resistance of any substance per degree of temperature change.

Let us take a conductor having a resistance of R0 at 0oC and Rt at toC respectively.

From the equation of resistance variation with temperature we get

Rt / Ro = to +t/ t0 +0

Rt = Ro + Ro.t/to

Rt – Ro = Ro . t/to

∆R = 1/to . Ro . t = αo Ro . t

This αo is called temperature coefficient of resistance of that substance at 0oC

The change in electrical resistance of any substance due to temperature mainly depends upon three factors –

- The value of resistance at initial temperature,
- The rise of temperature and
- The temperature coefficient of resistance αo.

The temperature coefficient of resistance of a material is also changes with temperature.

If αo is the temperature coefficient of resistance of material at 0oC, then from equation (2), the resistance of material at toC,

Rt = Ro [ 1+αo(t)]

where, R0 is the Resistance of material at 0oC

Similarly, if the temperature coefficient of resistance of material at toC is αt, then the resistance of the material at 0oC is

Ro = Rt[ 1+αt(-t)]

Resistance variation with temperature:

Resistance of conductor, R=Ro(1+αΔT) where ΔT=T−To

⟹ R=Ro+RoαΔT

We get slope of line, m=Roα

⟹ Temperature co-efficient, α=m/Ro

The resistivity of these materials is highly dependable upon their temperature. Generally, metals offer more electrical resistance if temperature is increased.

On the other hand, the resistance offered by a non-metallic substance normally decreases with increase of temperature.

Examples:

In the circuit below resistors R1 and R2 are in series and have resistances of 5 Ω and 10 Ω, respectively. The voltage across resistor R1 is equal to 4 V. Find the current passing through resistor R2 and the voltage across the same resistor.

We use Ohm's law V = R I

To find the current I1 passing through R1.

4 = 5 I1

Solve for I1

I1 = 4 / 5 = 0.8 A

The two resistors are in series and therefore the same current passes through them.

Hence the current I2 through R2 is equal to 0.8 A.

We now use Ohm's law to find the voltage V2 across resistor R2.

V2 = R2 I2 = 10 (0.8) = 8 V

2.The resistance of a wire is 20 Ω. What will be new resistance, if it is stretched uniformly 8 times its original length?

Solution

R1 = 20 Ω, R2= ?

Let the original length (l1) be l.

The new length, l2 = 8l1 (i.,e) l2 =8l

The original resistance, R = ρ [ l1 / A1]

The new resistance

R2 = . l2/ A2 = (8l)/ A2

Though the wire is stretched, its volume is unchanged.

Initial volume = Final volume

A1.l1= A2.l2 ,

A1.1 = A2 .8l

A1 / A2 = 8l / l = 8

By dividing equation R2 by equation R1, we get

R2/R1 = (8l)/ A2 x A1/ l

R2/ R1 = A1/A2 x 8

Substituting the value of A1/A2, we get

R2 / R1 = 8 ×8 = 64

R2 = 64 × 20=1280 Ω

Hence, stretching the length of the wire has increased its resistance.

3.A small light bulb is connected to a 6 V battery and draws 2 A of current. What is the net resistance of the bulb?

- Voltage: V = 6 V
- Current: I = 2 A
- Resistance: R = ?

Since R is unknown, .

- R = V/I

- R = 6/2
- R = 3 Ω

Determine the amount of current going through a 50 Ω; resistor with a voltage of 120 V.

- Resistance: R = 50 Ω
- Voltage: V = 120 V
- Current: I = ?

Since I is unknown

- I = V/R

I = 120/50

I = 2.4 A

References:

Basic Electronics by Chattopadhyay, D.

- Getting started in Electronics by Forrest Mims

How to Diagnose and Fix Everything Electronic, Second Edition

Book by Michael Jay Geier