RESISTIVITY AND CONDUCTIVITY
Resistivity is the measure of opposition to the flow of current while Resistance is the opposition to current. The resistance of a material depends on four main factors
- Length of the material: the longer the material the higher its resistance in other words, the resistance of a material is directly proportional to the length of that material i.e. R α L
- Area of cross section: the resistance of a material varies inversely with the area of cross section. i.e. the smaller the area the bigger the resistance i.e. R α 1/A
- Nature of material: Some materials naturally have high resistance for example between copper and aluminium, aluminum has a higher resistance than copper that is why copper is a better conductor than aluminum.
- Temperature: The resistance of metals generally increases with temperature i.e. metals are good conductors at low temperature. At higher temperature they have higher resistance and they tend to become poor conductor. Generally RF = R0(1 + αθ), Where α is called the temperature coefficient of the metal, RF is the final resistance while Ro is the original resistance. At low temperature, the molecules of metal are orderly; hence they allow the passage of current i.e. low resistance. When they are heated, their molecules become energetic moving around randomly and preventing the passage of current (high resistance). Metals are therefore said to have positive temperature coefficient for resistance.
This is the measure of the rate at which current flow through the material. Any material that allow the flow of current through it is called a conductor. Conductivity is the reciprocal of resistivity.
Any Material that do not allow the flow of current through it is called a Resistor. Resistors can be arranged in two ways
- Series arrangement: the following points should be noted of resistors in series
- Equal amounts of current flow through them.
- Total voltage in a circuit is equal to the sum of the potential difference across the resistors
IR = IR1 + IR2 + IR3
IR = I(R1 + R2 +R3)
R = R1 + R2 + R3
- Parallel arrangement : the following points should be noted of resistors arrange in parallel
- They have equal voltage or potential difference.
- Total current in a circuit is equal to the sum of current through the resistors.
Electrical Energy can be defined as the product of the charge transported and the potential difference between the points of transfer. The following are the formulae for calculating Electrical Energy
Electrical Energy=qv ……………….(1)
But q = IT
Electrical energy = VIT…………….(2)
But V = IR
Electrical energy = I²RT……………(3)
Electrical power can be defined as the rate at which electrical energy is expended. The following are the formulae for calculating Electrical Power
Electrical power = VI……………..(6)
Electrical power = I²R……………..(7)
NB: the mark 100W, 220V on an electric bulb means that the bulb has a power of 100 W and the potential difference applied across the terminals of the bulb is 220V.
The commercial unit of electrical energy and power is kilowatt hour (KWh). The cost of electricity can be obtained by multiplying the kilowatt hour consumed and the unit of electricity.
In transmitting power from a mega station to a soft station, effort must be made to ensure that power loss is minimized. This can be achieve in two major ways.
- Transmitting power at high voltage and low current. This is called high tension transmission (HTT)
- By using cables of low resistances.
When power is been transported from one point to another, some amount of it is been lost. The lost power can be calculated by
Power loss= I²R, where R is the resistance of the cable. For domestic power consumption, the high voltage coming from the soft station must be reduce by using a step down transformer.
Electric current have so many effect of substances. Some of these effects include: Chemical effect, Mechanical effect, Magnetic effect, Sound effect, light effects, Heating Effect.
The resistance of a material makes it possible for electrical energy to be converted to heat. The following equations explain the energy conversion
Electrical energy= heat energy
Pt=mcθ=ml
VIt= mcθ= ml
I²RT= mcθ =ml
This is a safety device used for preventing excess current from destroying an appliance. An electric Fuse must have low melting point so that it can melt when high current flow through them). A fuse must be connected to the live terminal end.
Fuse rating is the maximum safe current permitted to flow in it before the fuse breaks.
Electrical appliance must be connected in parallel so that they can use the same voltage and the malfunctioning of one will not affect the operation of the other.
This is a device used for detecting the direction of flow of current. The following are the essential components of a galvanometer
1. Horse shoe magnets: this provides a magnetic field
2. Soft iron cylinder: to improve the strength of the magnetic field and to make it radial
3. Control spring: this provides opposing couple and returns the pointer to the zero mark when current stops flowing.
4. Scale: this gives the reading of the current measured
5. Pointer: this moves round the scale when current begins to flow through the device.
6. Rectangular coil: These serves as the current carrying conductor.
A galvanometer is said to be sensitive if it can detect small amount of Current.
Where n is the number of turns in the coil of the galvanometer, B is the magnetic field around the coil, A is the area of the coil, c is the restoring torque per unit twist, I is the current.
The sensitivity of a galvanometer can be enhance by
1. Using a very strong magnets
2. Using coil of long area
3. Increasing the number of turns in the coil
4. Using a weak control spring
A galvanometer is said to be accurate if the value it gives is identical to the value obtained from a standard measuring device.
A shunt can be defined as a low resistance resistor place in parallel with a galvanometer in other to convert it to an ammeter.
p.d across shunt = p.d across galvanometer
(I – IG)Rs = IGRG
Where RS is the resistance of the shunt; IG is the maximum allowable current through the galvanometer or maximum current for full scale reading.
A multiplier is a high resistance resistor place in series with a galvanometer in other to convert it to voltmeter.
Examples
- The resistance of a piece of wire of length 20m and cross sectional area 8 × 10⁻⁶m² is? (resistivity of wire = 4 × 10⁻⁷ Ωm)
- A wire of length 15m made of a wire of resistivity 1.8 ×10⁻⁶Ωm has a resistance of 0.27 Ω. Determine the area of the wire.
- An ammeter of resistance 5Ω have a full scale deflection when a current of 50mA flows in it, the value of the resistor require to adapt it to measure a current of 5A is
- A galvanometer of resistance 10Ω has a full scale deflection with a current of 10mA. Calculate the magnitude of the resistance required to convert it to a voltmeter capable of measuring up to 3v.
- A moving coil galvanometer has a full-scale deflection of 3A equivalent to 30° deflection. The sensitivity of the instrument is
Solution
- A generator is on a daily use and in the process ten 60 watt and five 40watt bulbs are on for the same time interval, the energy consumed daily is
- If NEPA charges 5k per KWh. What is the cost of operating for 24hrs a lamp requiring 1A on a 220V line?
- A 40KW electric cable is use to transmit electricity through a resistor of resistance 2Ω at 800V. The power loss is
Solution
- In the diagram below. X and Y are resistance 4Ω and 6Ω respectively. If the power dissipation in X is 10W, then the power dissipation in Y is
- Find the effective resistance in the diagram below
Solution
Since the resistors are in series,
R = 4Ω +4Ω+4Ω+4Ω+4Ω+4Ω = 24Ω
Exercises
- A wire of 5Ω resistance is drawn out so that its new length is two times the original length. If the resistivity of the wire remains the same and the cross sectional area is halved, the new resistance is ?
- An electric heater with a potential difference of 240V connected across its terminal has a total resistance of 980Ω. Find the power rating of the heater
- An electric device is rated 2000W, 250V. The current fuse rating of the device is?
- If NEPA charges 5k per KWh. What is the cost of operating for 24hrs a lamp requiring 1A on a 220V line?
- A landlord has eight 40W electric light bulbs, four 60W bulbs and two 100 W bulbs in his house. If he has all the points on five hours daily and if NEPA charges 5k per unit, his bill for 30days is?
- All the heat generated in a 5ohms resistor by 2A flowing for 30seconds is used to evaporate 5g of a liquid at its boiling point. What is the specific latent heat of the liquid?
- An electric iron is rated at 1000W, 250 V. The corresponding maximum resistance and accompanying current is ?
- An electric current of 3A flowing through an electric heating element of resistance 20 embedded in 1000g of an oil raises the temperature of the oil by 10°c in 10seconds. The specific heat capacity of the oil is ?
- The resistance of a 240V, 60W electric filament bulb is ?
- A standby generator is connected to fifteen 40W lamps and a musician 600W amplifying system. How much energy is used if the generator runs for 6hrs?
- Electricity is supplied to a school along a cable of total resistance 0.5Ω with the maximum current drawn from the mains as 100A. The maximum energy dissipated as heat for 1hour is ?
- Electrical power is transmitted at a high voltage rather than low voltage because the amount of energy loss is reduce due to (a)Heat dessipation(b) production of Eddy current (c) Excessive current discharge (d) excessive voltage discharge
- Which of the following is an essential physical properties of the wire used for making fuses (a) low density (b)high thermal conductivity (c)low electrical resistivity (d) low melting point
- The primary aim in high tension transmission is to (a)minimize energy losses due to heat production (b)increase the rate of energy transfer by using high voltage (c) increase the current in the wires(d) generate electricity at high current and low voltage
- Find the cost of running a 60W lamp for 24hrs, if 1KWh cost 5naira
- A lamp is rated 240V 60W. Calculate the resistance of it's filament.
- The maximum power dissipated by a 100Ω resistor in a circuit is 4W; calculate the voltage across the resistor.