Resistance

Resistors

Resistance is a property of all materials, it is a measure of how hard it is for current to flow through a material or device. The higher the resistance the less current is able to flow. Materials with very high resistances are called insulators, those with low enough resistances to allow a current flow are termed conductors.

The resistance of components in electrical circuits is measured in Ohms (Ω). All components have some resistance to the flow of current, even the cells and batteries. Some devices are designed to have a high resistance and even variable resistances. A filament bulb for example has a thin wire that is intended to have a high resistance, it is this resistance to the current that causes it to glow and give out light.

A fixed resistor is a very small plastic coated component that can be used to reduce the current in parts of a circuit, often to protect sensitive devices from large currents.

The colour stripes on the resistor indicate the level of resistance in ohms.

Ohms Law

Ohm’s Law states that the current through a conductor is proportional to the voltage across it. This means that for a given component, like a bulb, the current will increase as the voltage increases. If the voltage is kept constant but the resistance is increased then the current will reduce.

Ohm’s Law can be summarized as:

Ohm’s Law can be summarized as:

_Voltage = Current x resistance or V = IR _

Where V is voltage in Volts (V), I is current in amps (A) and R is resistance in Ohms (Ω)

This can be demonstrated with a simple series circuit by adding additional bulbs one at a time. As each bulb adds more resistance to the circuit the current reduces and the bulbs get dimmer and dimmer. Adding another cell to the circuit will increase the voltage and the bulbs will get brighter as the voltage increases.

Worked Examples.

Calculate the voltage required to produce a 3 A current in a series circuit with a 2 Ω resistance.

V = IR = 3 A x 2 Ω = 6 V

What is the resistance of a bulb if a 3 V battery of cells produces a current of 0.25 A?

V =IR, therefore R =V÷ I = 3 V ÷ 0.25 A = 12 Ω

Addition of Resistors

Resistors in Series

When a current has to pass through a set of resistors arranged in series, the effect of all the individual resistors are added together. As the current only has one route it must pass through all the resistors in turn. They act like one single larger resistor.

Total resistance = Sum of the individual resistors.

R_t = R₁ + R₂ +R₃

Resistors in Parallel

When the resistors are arranged in parallel the current has different routes, in this situation each resistor contributes only a fraction of the total resistance proportional to its own resistance. More current will flow through the branch with the least resistance and less through the branches with higher resistances.

The inverse of the total resistance can be calculated as follows:

when the fractions have been added the result is inverted to find R_t

Worked Examples

Compare the Total Resistance of a 2 and a 3 resistors in series with the same resistors in parallel.

__Series __

R_t =R₁ +R₂ = 2 + 3 = 5Ω

Parallel

Effect of Components on Current

Different components will have varying effects on the current that can flow in a circuits. All components add resistance and will, therefore, in accordance with Ohm’s Law reduce the current for a given supplied voltage.

1. Filament bulbs have a thin length of wire, normally made from tungsten inside a glass bulb from which the air has been removed

As the current passes through the wire it begins to glow due to the high resistance caused by thin wires. This produces heat and that in turns makes the wire white hot and it begins to emit visible light.

As the potential difference (voltage) is increased the electrons get more force applied to them and so they increase their rate of flow, resulting in a higher current. This also increases the temperature of the wire and leads to a reduction in the wires resistance. So as the potential difference increases the current increases rapidly as a result of both the higher voltage and the lowering of the resistance.

1. Diodes can be thought of as one way values for an electrical circuit.

The diode will allow a current to flow provided the polarity of the potential difference is correct, they have very low resistances so have only a minor impact on the current provided the Anode potential is greater than the cathode potential. If the potential differences is reversed then no current will flow in that part of the circuit.

1. Fixed Resistors are designed to have a specific resistance that can not be changed, Therefore, as the potential difference is increased the flow of current will increase in proportion to the increase in potential difference or voltage. The higher the voltage the higher the current.

They obey Ohm’s Law Current = Voltage Resistance.

Light Dependent Resistors

A light Dependent Resistor (LDR) is a form of variable resistor, It responds to the surrounding light levels and changes its resistance in different light conditions. As the light intensity increases the additional energy supplied by the light reduces the resistance of the material in the LDR. This results in__ the resistance decreases as the light levels increase__.

The graph illustrates the relationship between light intensity and the resistance of a typical LDR.

LDRs can be used in many devices, including as part of a car’s automatic headlamps, or a security light that only activates in the dark.

Thermistors

Thermistors are another example of a variable resistor, they are sensitive to temperature changes. As the temperature increases close to the thermistor the additional energy reduces the resistance of the material so a greater current can flow. For a thermistor the higher the temperature the lower the resistance.

The graph illustrates the resistance of a thermistor as temperature increase.

Thermistors can be used in circuits that control temperatures, they are found in digital thermostats connected to central heating systems and in temperature controls of fridges and cookers.

What is the resistance of an electrical motor connected to the mains supply at 40 A?

5.75
Explanation: UK mains 230 V V=IR so R = V I = 230 40 = 5.75 Ω

What is the current in a circuit where two 2 bulbs are wired in series with a 4V cell?

Your answer should include: 1A / 1
Explanation: V= IR so I = VR = 4 (2 + 2) = 1 A

Explain what would happen to a bulb wired in series with a diode and a cell if the cells direction was reverse.

out
Explanation: The bulb would go out, because reversing the cell reverses the polarity of the potential difference, the diode will not allow a current to flow in this situation, thus the bulb would not come on as no current is flowing.