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Resistance is a physical quantity that measures the resistance offered by any object to the flow of electric current. In other words, resistance is the ability of an object to resist the flow of electrons in a circuit. The concept of resistance can be best understood by imagining a person in a crowded market struggling to go from one shop to another. This is identical to an electron trying to make its way through a wire, and the opposition faced by the person can be understood as resistance.
In physics, the formula for resistance is equal to the voltage applied to the resistor to the current flowing through it.
Mathematically, the resistance formula is given as: R=V/I.
- Here, V is the Voltage across the resistor, R is the Resistance, and I is the Current flowing through an electric circuit.
- A resistor is an electronic component in a circuit that provides a specific amount of resistance.
- The SI unit of resistance is ohms (Ω), denoted by the Greek uppercase letter omega.
- Electrical resistance measures the opposition offered by a device to the flow of current through it.
Key Summary
In this article, we will discuss in detail the important physical quantity in physics, i.e., resistance and the resistance formula.
- The property of materials that allows the flow of electric current is referred to as resistance. The flow of electrons in a circuit is called electric current (denoted by I).
- The resistance formula is explained here with the help of Ohm's law, according to which the voltage across the resistor is equal to the product of the resistance and the current flowing through it.
- The value of resistance for a conductor, an insulator, and a semiconductor varies.
What is Resistance?
Resistance, also called electrical resistance, is the property of a material that opposes the flow of electric current through it. Resistance acts in the same way that friction does in a circuit. Electrical resistance, like friction, opposes the flow of current through a wire in the same way that friction opposes free and easy motion. It is denoted by the letter R, and the value depends on the current flowing through a resistor and the voltage across it.
- Resistance is the opposition to current flow in an electrical circuit.
- The inverse quantity of electrical resistance is electrical conductance.
- Electrical conductance is the ease with which the electrical current passes through an object.
Types of Materials and their Resistance
The German scientist George Simon Ohm is credited with unveiling the resistance formula and the relationship between voltage and current flowing through the circuit. He explained the concept by proposing Ohm’s law and giving the resistance formula. The value of resistance varies for different materials, such as:
Resistance Formula in Conductors:
Those substances in which electric current can flow easily are called conductors. Thus, conductors allow very little resistance. Examples of conductors include Silver, copper, gold, etc.
The resistance formula in conductors is given as: R=ρL/A (R= Resistance; ρ= Resistivity; L= Length of wire; A= Area of cross-section)
Resistance Formula in Insulators:
Those substances in which electric current can not flow easily are called insulators. Thus, insulators offer high resistance that opposes the flow of electrons. The examples of insulators are rubber, paper, glass, etc.
The resistance formula in insulators is given as: R=ρL/A (R= Resistance; ρ= Resistivity; L= Length of wire; A= Area of cross-section)
Resistance Formula in Semiconductors:
Those substances in which there is a partial flow of electrons are called semiconductors. The resistance of semiconductors is dependent on temperature. With a decrease in temperature, the resistance of the semiconductor increases, and vice versa.
The resistance formula in semiconductors is given as: R=ρL/A (R= Resistance; ρ= Resistivity; L= Length of wire; A= Area of cross-section)
Resistance Formula Comparison Table
The resistance formula in conductors, insulators, and semiconductors is given below in tabular format:
| Characteristics | Conductor | Insulator | Semiconductor |
|---|---|---|---|
| Resistance Formula | R=ρL/A | R=ρL/A | R=ρL/A |
| Resistivity (ρ) | Very low (10-8Ωm) | Very high (10-10–10-16 Ωm) | Moderate (10-5–103 Ωm) |
| Effect of Temperature & Resistance | Resistance increases with a rise in temperature | Resistance decreases with a rise in temperature | Resistance decreases sharply with a rise in temperature |
| Examples | Copper, Silver | Rubber, Glass | Silicon, Germanium |
Discover the Chapter video:
Current Electricity Detailed Video Explanation:
Resistance Formula & Ohm’s Law
Ohm's law can be used to calculate the electrical resistance formula of a given system. Ohm's law is a well-known practical law of circuit physics.
| “Current flowing through a circuit is directly proportional to the voltage applied across it and inversely proportional to the resistance provided by the wire, assuming that the temperature remains constant.”Ohm’s Law |
From Ohm’s law, the resistance formula can be expressed as:
| V ∝ I V = IR R=V/I |
Here,
- V denotes the applied voltage.
- I represent the current.
- R denotes electrical resistance.
From the resistance formula, we can also get the dimension of resistance, which is expressed as [M1L2T-3I-2M]
Here, M=Mass, L=Length, T = Time, I = Current
Significance of Ohm’s Law in Resistance Formula
Ohm's law in physics establishes the relationship between the resistance (R), the current flowing in the circuit (I), and the applied voltage (V) across the resistor. This gives us the resistance formula, i.e., R=V/I. Thus, Ohm's law in physics has three significances:
Possibility 1: If both voltage and current are known, the above formula can be used to calculate the electrical resistance.
Possibility 2: If both voltage and resistance are known, the above formula can be used to calculate the current.
Possibility 3: If both resistance and current are known, the above formula can be used to calculate the voltage.
The video below explains this:
Resistance Formula Detailed Video Explanation:
Solved Examples on Resistance FormulaQues. A circuit has a voltage of 12 volts and a current of 2 amperes. What is the resistance of the circuit? Solution: Using the resistance formula R=V/I We can find the resistance of the circuit as: R=V/I where R is the resistance, V is the voltage, and I is the current. Substituting the given values, we get: R=12V/2A R = 6 ohms Therefore, the resistance of the circuit is 6 ohms. Note: In practice, the voltage and current of a circuit may vary over time. In such cases, the resistance of the circuit is usually calculated as the ratio of the average voltage to the average current over a certain period of time. Ques. What will be the value of voltage (V) if the current flowing in the circuit (I) is 2 amperes, and the resistance offered by the body (R) is 4 ohms? Ans. Here, the given values are: Current (I) = 2A, Resistance (R) = 4Ω From Ohm’s law, we have V = IR------(i) By substituting the given values in equation (i), we get: V = 2 x 4 = 8 V Therefore, the value of voltage in the circuit is 8 V. |
Also check:
Derivation of Resistance Formula
When three resistors are connected in series, the same current flows through each resistor, but the voltage drop varies. If V is the applied voltage and V1, V2, and V3 are the voltages across the resistances R1, R2, and R3, respectively, then
V = V1 + V2 + V3 ...(1)
Ohm's law states that V = IR
Req = R1 + R2 + R3
As a result, the equivalent resistance or total resistance of the circuit is a single value of resistance that can replace any number of resistors connected in series without changing the value of the circuit's current or voltage.
If we have n series resistances, the generalised formula for equivalent resistance is
Req = R1 + R2 + R3.......+ Rn
We already know that the applied voltage is (v)
∴ V = V1 + V2 + V3
We also know that
V = IR (from Ohm’s law)
⇒ IReq = I(R1 + R2 + R3)
⇒ R1 + R2 + R3
As a result, the equivalent resistance or total resistance of the circuit can be defined as a single value of the resistor connected in series, by changing the values of the circuit's current or voltage.
Factors Affecting Electrical Resistance Formula
A conductor's electrical resistance formula is determined by the following factors:
- The cross-sectional area of the conductor
- The length of the conductor
- The material of the conductor and the temperature
The electrical resistance is proportional to the length of the conductor (L) and inversely proportional to the cross-sectional area (A). It is denoted by the following relationship.
| R=ρL/A |
where ρ is the material's resistivity (measured in ohms per metre)
Resistivity in Resistance Formula
The ability of a material to resist the flow of electric current is measured qualitatively as resistivity in the resistance formula. Insulators, by definition, have higher resistivity than conductors. The S.I unit of resistivity in the resistance formula is ohm metre, which is represented as Ωm.
For comparison, the resistivities of a few materials are listed below. Always keep a note that materials with a low resistivity value conduct electricity very well.
- Silver – 1.00×10−8 Ωm
- Copper – 1.68×10−8 Ωm
- Aluminium – 2.82×10−8 Ωm
- Wood – 1.00×10−14 Ωm
- Air – 2.30×1016 Ωm
- Teflon – 1.00×1023 Ωm
Also Read
PotentiometerResistivity & Current Density in Resistance Formula
Electric resistivity, denoted by, is defined as the electrical resistance offered per unit length and unit cross-sectional area at a specific temperature. Specific electrical resistance is another name for electrical resistance. Ohms. The metre is the SI unit of electrical resistivity. The electrical resistivity formula in terms of current density is given as:
| ρ=E/J |
Where,
- ρ is the material's resistivity expressed inmetrese
- E represents the electric field in V.m-1
- J represents the current density in A.m-2.
Difference Between Resistance and Resistivity
The difference between the resistance formula and resistivity is explained below in detail:
| Resistance | Resistivity |
|---|---|
| Resistance occurs when the flow of electrons in a material is opposed. | Electrical resistivity is the property of a material that measures how strongly it resists electric current |
| The resistance formula is given as R=V/I | The Resistivity Formula is given as ρ=E/J |
| It is denoted by the unit Ohms. | It is measured in Ohms. metre. |
| Its symbol is R. | Resistivity is denoted by ρ. |
| It depends on the conductor's length and cross-sectional area, as well as the temperature. | Resistivity depends on temperature. |
Things to Remember
- Resistance is the property of a material that restricts the flow of electric current.
- The formula for resistance is R=VI, where R is resistance, V is voltage, and I is current.
- The unit of resistance is the ohm, which is defined as the amount of resistance that limits the flow of one ampere of current when one volt of voltage is applied.
- The resistance of a material depends on its resistivity, which is a measure of the material's ability to resist the flow of electric current.
- The resistivity is affected by factors such as temperature, impurities, and the material's composition.
- The resistance formula can be used to calculate the resistance of a circuit and in the design and analysis of electrical systems.
- For example, it can be used to calculate the resistance of a resistor or a wire or to determine the total resistance of a series or parallel circuit.
Ques 1: Calculate the resistance provided by the body if 2mA of current flows with a potential difference of 2V. (3 marks)
Ans: Given: I (Current) = 2 mA
V = 2 V (Potential difference)
By applying the resistance formula-
R=V/I
, we get:
= 2/2 ×10−3
= 1000Ω
Ques 2: Determine the resistance when 5Ω and 2Ω are connected in parallel. (3 marks)
Ans: Resistances are given as:
R1 = 5 Ω,
R2 = 2 Ω
The parallel resistance is articulated as
(R1R2)/(R1+R2)
= 1.428Ω
Ques 3: Consider a 10 resistor in a circuit with a current of 2 amps and a voltage of 120 volts. How much voltage is lost across the resistor? (3 marks)
Ans: Using Ohm's triangle, we can see that:
V = IR
2 x 10 = 20 V
The difference, i.e., 120 - 20 = 100 V, is lost across the resistor.
Ques 4: How to Apply Ohm's Law to Different Parameters?
Ans: Ohm's law is used to calculate current, resistance formula, and potential difference. The 3 formulas in Ohm's law are.
- Voltage Detection (V) – V = IR
- Calculating Current (I) – I = V/R
- Calculating Resistance (R) – V/I = R
Ques 5: In an electric circuit, a current of 4.00 A flows through a resistor. The voltage drop, which takes place from one end of the resistor to the other, happens to be 120 V. Find out the value of the resistance. (3 marks)
Ans: Applying the resistance formula
R = V/I
So, R = 120V/4A
R = 30 Ω
Hence, the resistance of the resistor in the circuit is 30.0 Ω.
Ques 6: What is the formula to find the specific resistance ρ? (3 Marks)
Ans: The formula to find the specific resistance ρ is given as:
R=ρL/A
Where:
- ρ is the resistivity of the material in ohm metres, Ω-m
- R is the electrical resistance of a uniform specimen of the material measured in ohms
- l is the length of the piece of material measured in metres, m
- A is the cross-sectional area of the specimen measured in square metres, m2
Ques 7: In the inductive circuit, when inductance (L) or inductive reactance (XL) increases, the circuit current decreases. Give reasons. (3 Marks)
Ans: The current in an inductive circuit is given by:
I = V/XL
- where I = Current
- V = Voltage
- XL = Inductive reactance
Explanation:
- XL is inversely proportional to the current.
- Hence, with an increase in inductive reactance, the current decreases.
Ques 8: List down the factors that affect the resistivity of electrical conductors. (4 Marks)
Ans: Resistivity is the property of a conductor that opposes the flow of electric current through it. It is independent of the shape and size of the materials, but it depends on the nature and temperature of the materials is called resistivity.
- The unit for resistivity is the ohm-meter (Ω-m).
- The resistivity of a material depends on its nature and the temperature of the conductor.
- The resistivity of a material doesn't depend on its shape and size (length and area).
- The resistivity of the conductor increases as the temperature increases.
The resistivity of any material depends on the temperature as ⇒ ρt = ρ0 [1 + α (T - T0)]
where, ρ0 = resistivity at standard temperature, ρt = resistivity at temperature t0 C, T0 = reference temperature, α = the temperature coefficient of resistivity.
- The resistivity of a material doesn't depend on its shape and size (length and area).
- The resistivity of the conductor increases as the temperature increases.
Ques 9: An electric cabin heater draws 15 A at 110 V. If the voltage is reduced to 95 V, calculate the current. (4 Marks)
Ans: We can use the principle of power conservation to solve this problem. The power consumed by the electric cabin heater is the product of the voltage and the current, given by P = VI. Since the heater is designed to produce a certain amount of heat, the power consumed should remain constant, even if the voltage is changed. Therefore, we can use the equation P = VI to solve for the current when the voltage is changed.
When the heater is operating at 110 V, the current is 15 A. Therefore, the power consumed is:
P = VI = (110 V)(15 A) = 1650 W
When the voltage is reduced to 95 V, we can solve for the current using the same equation:
P = VI
Solving for I, we get:
I = P/V = 1650 W/95 V = 17.37 A
Therefore, when the voltage is reduced to 95 V, the current drawn by the electric cabin heater increases to 17.37 A.
Ques 10: Three resistors of 3 ohms, 10 ohms, and 15 ohms are connected in parallel in a 30 V circuit. The current that flows through the 3-ohm resistor is 10A. Explain. (5 Marks)
Ans: When resistors are connected in parallel, the voltage across each resistor is the same, while the current is divided among the resistors. The total current in the circuit is the sum of the currents in each resistor. We can use Ohm's law to find the current in each resistor:
I = V/R
where I is the current, V is the voltage, and R is the resistance.
In this case, the three resistors are connected in parallel, so the voltage across each resistor is 30 V. We are given that the current through the 3-ohm resistor is 10 A, so we can use Ohm's law to find the equivalent resistance of the other two resistors in parallel:
10 A = 30 V / 3 Ω
30 Ω = 30 V / 10 A
The equivalent resistance of the two remaining resistors is:
1 / (1/10 Ω + 1/15 Ω) = 6 Ω
Now that we have the equivalent resistance, we can use Ohm's law to find the total current in the circuit:
I = V / R = 30 V / (3 Ω + 6 Ω) = 3.33 A
The total current in the circuit is 3.33 A. Since the resistors are connected in parallel, the current through each resistor is proportional to its resistance. We can use the ratio of the resistance of the 3-ohm resistor to the total resistance of the circuit to find the current through the 3-ohm resistor:
I(3 Ω) = (3 Ω / (3 Ω + 6 Ω)) * 3.33 A = 1.11 A
Therefore, the current that flows through the 3-ohm resistor is 1.11 A.
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