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Electricity plays a huge role in our day-to-day life. Most of the work done today uses electricity as a basic medium. From providing us with light to helping us charge electronic gadgets, electricity is the most convenient form of energy. Electricity or current refers to the flow of charge through a cross-sectional area in a given period of time. Mathematically,
Current (I)= Q/T,
Here Q represents the number of charges that flow through the material in a given time (T).
Let’s recall some of the important terms that will help us understand resistivity
- Materials can be differentiated based on their behavior when current passes through them. Thus, materials can be classified into three categories, namely conductors, semiconductors, and insulators.
- Conductors are material through which current can flow easily with less hindrance, whereas insulators oppose the flow of current.
- Conductivity is the intrinsic property of a material. It gives us an idea about how much current a material can carry. It is also stated as the ratio of current density to electric field strength.
- Potential Difference is the measure of work done to displace one unit of charge from one point to another. Mathematically, potential difference- (V)=W/Q
- According to Ohm’s Law, resistance is the hindrance caused to the flow of current. Mathematically,
V = I / R
Here ‘V’ represents the potential difference,
‘I’ is the current,
and ‘R’ is the resistance.
This portion is a part of CBSE class 10 Unit 4 Effects of current carring a total weightage of 13 marks and 32 periods.
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Keyterms: Resistance, Ohm’s Law, Conductivity, Potential Difference, Current density, Elecrtric field, Conductor, Semi conductor
Electrical resistivity
[Click Here for Sample Questions]
Resistance is the measure of hindrance provided by the material during the flow of current when the temperature of the system is constant. Resistance helps to control the amount of current passing through a given material by opposing the flow of current.
According to Ohm’s law, current(I) flowing through a conductor is directly proportional to the potential difference between the two ends of the material keeping current constant.
Mathematically, V ∝ I
V=IR (R is the proportionality constant, known as Resistance)
=>R=V/I
SI unit of resistance is Ohm
The magnitude of this resistance is known as resistivity. Thus, resistivity is the intrinsic property of a material which gives us the measure of the ability of a given material to oppose the flow of current.
Resistivity(ρ) is inversely proportional to conductivity.
SI unit of resistivity is (ohm.m )
CGS unit of resistivity is (ohm.cm)
- Metals can be said to be good conductors of electricity. As we know, resistivity is the reciprocal of conductivity, thus metals have low resistivity. That is, metals allow the flow of current instead of providing high resistance or hindrance to it.
- Insulators (graphite, rubber, etc) are poor conductors of electricity. This means, the insulator opposes the flow of current instead of allowing it. Due to this, insulators have high resistivity and low conductivity.
- The last type of material is semiconductors. These are neither good conductors nor good insulators. Semiconductor’s resistivity changes proportionally with temperature. The resistivity of semiconductors also depends on the impurities present inside the material.
A list of materials with their resistivity at a constant temperature is given below.
Mathematically,
Resistivity (ρ) = E/J
Here, E denotes an electric field’s magnitude. (SI unit is V/m )
J represents current density. (SI unit is A/m2)
The resistivity of conductors having a uniform cross-section and uniform flow of current is mathematically given by
(ρ)=Rl/A
Here, R is the resistance of the material,
l is the length of the material and
A refers to the area of cross-section of the material.
The resistivity of any material depends on:
- Nature of the material, that is the length and area of the given material.
- Temperature.
Sample Questions
Question: What is the dimension of resistivity? (1 mark)
Ans. Dimension of resistivity is :
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Question: If a wire’s length is halved and you double its cross-sectional area. What would the effect be on the resistance of the wire if initially, it is R? (1 mark)
Ans. 1/4R :
R1=VI or (ρl)/a
R2={ρ(0.5)l} / 2a =(ρl/4a)
Thus R2=R1/4
Question: Derive the formula of resistivity ? (1 mark)
Ans. Resistivity can be explained as the resistance offered per unit length and cross-sectional area at a specific temperature.
R = ρ L / A
therefore, ρ = R A / L,
where R is the resistance in ohms,
A is the area of the cross-section in square meters
and L is the length in meters
Question. Show how resistivity varies with the properties of the material. (1 mark)
Ans. Resistivity varies with the properties of a material. With an increase in the length of material, resistivity decreases. From this, we can say that resistivity is inversely proportional to the length of the material. Similarly, with an increase in area, the resistivity of the material will also increase. Thus, it can be said resistivity is directly proportional to the area of the material.
Question. Two conductors A and B of length 5cm and 8cm respectively are given. Which among these shows higher resistance to the flow of current and why? (1 mark)
Ans. Conductor A will have less resistance than conductor B. We know, the resistance varies proportionally with the length of the material. Thus, the conductor of length 8cm will show more resistivity than conductor A.
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