Resistors and Resistance – SmartStudent Academy

Resistors are used to regulate or control the magnitude of current and voltage in a circuit according to Ohms law. Resistors are great electrical components used to reduce current flow, adjust signal levels, divide voltages, bias active elements, and other uses.

Types of resistors

The common types of resistors are categorized into:

Fixed resistors
Variable resistors.

Fixed resistors:

Fixed resistors are the most common and widely used types of resistors. They are used in electronic circuits to set the right conditions, and their values are known during the design phase of the circuit. Also, they never require to be changed to adjust the circuit, just as their name has indicated. There are many other types of fixed resistors that will be discussed below.

Variable resistors:

A variable resistor is a resistor of which the electric resistance value can be adjusted either mechanically (potentiometer, rheostat) or electronically (digital potentiometer).

Variable resistors are used in an electronic circuit to adjust circuit resistance as a means to control the voltage or current within a circuit (as per Ohm’s Law).

It mainly consists of a resistance track and a wiper contact. The wiper contact moves along the resistance track when the adjustable component is adjusted.

The electrical resistance is varied by sliding a wiper contact along a resistance track. Sometimes the resistance is adjusted at preset value as required at the time of circuit building by adjusting screw attached to it and sometimes resistance can be adjusted as when required by controlling knob connected to it.

These types of resistors are designed with a fixed resistor element and a slider that taps into the main resistor element. This makes the component achieve three connections; two connections to the fixed element and the third is the slider. In this manner, it acts as a variable potential divider if all three connections are used. It is possible to connect to the slider and one end to provide a resistor with variable resistance.

Resistance:

Resistance is the opposition that a resistor offered to the flow of electric current through itself. The unit of resistance is ohm.

Ohm is defined as the resistance of a conductor when a potential difference or a voltage of one volt is applied across the conductor causes a current of one ampere to flow through the conductor. The symbol used to represent ohm is Ω

Ohm’s Law

This law gives the relationship between the voltage across a conductor and the current flowing through it.

Ohm’s law states that “the current flowing through a metal conductor is directly proportional to the potential difference across the ends of the wire provided that temperature and other physical conditions remain constant”

Mathematically,

V α I

So V /I = constant, this constant of proportionality is called resistance

V / I = Resistance (R)

Resistance is measured in ohms and given the symbol Ω

Examples

A current of 2m A flows through a conductor of resistance 2 kΩ. Calculate the voltage across the conductor.

Solution

V = IR = (2 × 10-3) × (2 × 103) = 4 V.

A wire of resistance 20Ω is connected across a battery of 5 V. What current is flowing in the circuit?

Solution
I = V/R
= 5 / 20 = 0.25 A

Ohmic and non-Ohmic conductors

Ohmic conductors are those that obey Ohms law(V α I) and a good example is nichrome wire i.e. the nichrome wire is not affected by temperature.

Non Ohmic Materials:

Non ohmic materials or conductors are those materials or conductors that do not obey ohms law. They are materials in which the current that flow through them do not. increased as the voltage connected across them is increased. They are also affected by temperature hence non-linear.

Examples Of Non Ohmic Conductors include :

Valves
Diodes
Transistors
Gases
Rectifiers

Factors affecting the resistance of a metallic conductor

Temperature – resistance increases with increase in temperature
Length of the conductor– increase in length increases resistance
Cross-sectional area– resistance is inversely proportional to the cross-sectional area of a conductor of the same material.

Resistivity of a material is numerically equal to the resistance of a material of unit length and unit cross-sectional area. It is symbolized by ρ and the units are ohmmeter (Ωm). It is given by the following formula;

ρ = AR /l

where A – cross-sectional area, R – resistance, l – length

Example

Given that the resistivity of nichrome is 1.1× 10^-6Ωm, what length of nichrome wire of diameter 0.42 mm is needed to make a resistance of 20 Ω?

Solution

ρ = AR /l, hence l = RA/ ρ
= 20 × 3.142 × (2.1×10^-4) / 1.1 × 10^-6
= 2.52 m

Electromotive Force And Internal Resistance

Electromotive force (e.m.f.) is the p.d across a cell when no current is being drawn from the cell. It is the energy provided by a cell or battery per coulomb of charge passing through it, it is measured in volts (V).

It is equal to the potential difference across the terminals of the cell when no current is flowing.

where

e = electromotive force in volts, V

E = energy in joules, J

Q = charge in coulombs, C

The p.d across the cell when the circuit is closed is referred to as the terminal voltage of the cell.

Batteries and cells have an internal resistance (r) which is measures in ohm’s (W). When electricity flows round a circuit the internal resistance of the cell itself resists the flow of current and so thermal (heat) energy is wasted in the cell itself. Internal resistance of a cell is therefore the resistance of flow of current that they generate

Where

e = electromotive force in volts, V

I = current in amperes, A

R = resistance of the load in the circuit in ohms, W

r = internal resistance of the cell in ohms, W

We can rearrange the above equation;

and then to

In this equation (V) appears which is the terminal potential difference, measured in volts (V). This is the potential difference across the terminals of the cell when current is flowing in the circuit, it is always less than the e.m.f. of the cell.

Examples

A cell drives a current of 0.6 A through a resistance of 2 Ω. if the value of resistance is increased to 7 Ω the current becomes 0.2 A.

calculate the value of e.m.f of the cell and its internal resistance.

Solution

Let the internal resistance be ‘r’ and e.m.f be ‘E’.

Using E = V + I r = IR + I r

Substitute for the two sets of values for I and R

E = 0.6 × (2 + 0.6 r) = 1.2 + 0.36 r

E = 0.6 × (7 × 0.2 r) = 1.4 + 0.12 r

Solving the two simultaneously, we have,

E = 1.5 v and R = 0.5 Ω

A battery consists of two identical cells, each of e.m.f 1.5 v and internal resistance of 0.6 Ω, connected in parallel. Calculate the current the battery drives through a 0.7 Ω resistor.

Solution

When two identical cells are connected in series, the equivalent e.m.f is equal to that of only one cell.

The equivalent internal resistance is equal to that of two such resistance connected in parallel.

Hence Req = R1 R2 / R1 + R2

= (0.6 × 0.6) / 0.6 + 0.6

= 0.36 / 1.2

= 0.3 Ω

Equivalent e.m.f =1.5 / (0.7 + 0.3)

= 1.5 A

Hence current flowing through 0.7 Ω resistor is 1.5 A

Difference Between Emf and P.D:

Electromotive force is the potential difference between the terminal of a cell when it is not delivering any current in an external circuit or when they cell is in an open circuit.

While potential difference two points is the work done In moving one coulomb of electricity from one point to the other. The unit of potential difference is volt.

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