Electromotive Force And Ohm’S Law - Current And Electricity - Change In Resistance Due To Increase In Temperature

Electromotive force and Ohm’s law - Current and Electricity - Change in resistance due to increase in temperature

Electromotive force (EMF) is the energy per unit charge supplied by a source like a battery or generator
It is measured in volts (V)
Ohm’s law relates the current flowing through a conductor to the voltage across it and the resistance offered by the conductor
Ohm’s law equation: V = IR, where V is the voltage, I is the current, and R is the resistance
Resistance is a property of a conductor that resists the flow of electric current
Resistance is measured in ohms (Ω)

Electromotive force and Ohm’s law (continued)

In a circuit, the EMF provided by the source pushes the electric charges to move
The current flows from the positive terminal of the source to the negative terminal
The opposition offered by the circuit components to the flow of current is called resistance
Ohm’s law states that the current through a conductor is directly proportional to the voltage across it, and inversely proportional to the resistance
Mathematically, Ohm’s law can be written as: I = V/R

Change in resistance due to increase in temperature

Resistance of a conductor increases with an increase in temperature
This phenomenon is known as the temperature coefficient of resistance
Most conductors have a positive temperature coefficient, which means their resistance increases with temperature
The amount of increase in resistance depends on the material
The temperature coefficient of resistance is expressed in terms of the resistance change per degree Celsius (Ω/°C) or the percentage change per degree Celsius (%/°C)

Example: Change in resistance due to temperature

Let’s consider a copper wire with a resistance of 10 ohms at 25°C
The temperature coefficient of resistance for copper is 0.0039 Ω/°C
If the temperature increases to 60°C, we can calculate the new resistance using the formula: R2 = R1 * (1 + α * ΔT)
R2 = 10 * (1 + 0.0039 * (60 - 25))
R2 ≈ 10.77 ohms

Derivation of Ohm’s law

Let’s derive Ohm’s law using basic principles of physics
Consider a conductor of length L and cross-sectional area A
Assume the conductor has a uniform resistance R
Apply a potential difference V across the conductor
The current flowing through the conductor is I
Using the equation R = ρL/A, where ρ is the resistivity of the material, we can rewrite it as: V = (ρL/A) * I
Simplifying, we find: V = (ρL/A) * I = IR

Power in electrical circuits

Power is the rate at which work is done or energy is transferred
In electrical circuits, power is given by the equation: P = VI
P is the power in watts (W), V is the voltage in volts (V), and I is the current in amperes (A)
Power can also be calculated using the equation: P = I^2R, where R is the resistance
Similarly, power can be expressed as: P = V^2/R

Example: Power calculation in a circuit

Consider a circuit with a voltage of 12V and a current of 2A
Using the equation P = VI, we can calculate the power: P = 12 * 2 = 24W
Alternatively, if the resistance in the circuit is 6 ohms, we can calculate power using P = I^2R: P = 2^2 * 6 = 24W
Both methods yield the same result, demonstrating the conservation of energy

Kirchhoff’s laws

Gustav Kirchhoff developed two laws that are fundamental to the analysis of electrical circuits
Kirchhoff’s first law, also known as the current law, states that the sum of currents entering a junction is equal to the sum of currents leaving the junction
This law is based on the conservation of charge
Kirchhoff’s second law, also known as the voltage law, states that the sum of the electromotive forces (EMFs) and potential differences around any closed loop in a circuit is equal to zero

Example: Application of Kirchhoff’s laws

Let’s consider a circuit with two resistors and a battery
According to Kirchhoff’s first law, the current entering the junction is equal to the current leaving the junction
According to Kirchhoff’s second law, the sum of the potential differences across the resistors and the EMF of the battery is equal to zero
We can use Kirchhoff’s laws to solve circuits with multiple components and understand the flow of current and potential differences

Resistance in series circuits

In a series circuit, the resistors are connected in a line, end to end
The total resistance in a series circuit is equal to the sum of the individual resistances
Mathematically, the formula for calculating the total resistance in a series circuit is: Rt = R1 + R2 + R3 + …
The current flowing through each resistor is the same in a series circuit
The voltage across each resistor can be calculated using Ohm’s law: V = IR

Example: Calculating total resistance in a series circuit

Let’s consider a series circuit with three resistors: R1 = 2 ohms, R2 = 3 ohms, R3 = 4 ohms
To find the total resistance, we add the individual resistances: Rt = 2 + 3 + 4 = 9 ohms

Resistance in parallel circuits

In a parallel circuit, the resistors are connected across each other, forming multiple pathways for the current to flow
The total resistance in a parallel circuit is the reciprocal of the sum of the reciprocals of the individual resistances
Mathematically, the formula for calculating the total resistance in a parallel circuit is: 1/Rt = 1/R1 + 1/R2 + 1/R3 + …
The voltage across each resistor in a parallel circuit is the same
The current flowing through each resistor can be calculated using Ohm’s law: I = V/R

Example: Calculating total resistance in a parallel circuit

Let’s consider a parallel circuit with three resistors: R1 = 2 ohms, R2 = 3 ohms, R3 = 4 ohms
To find the total resistance, we use the formula: 1/Rt = 1/2 + 1/3 + 1/4
Simplifying, we get: 1/Rt = 6/12 + 4/12 + 3/12 = 13/12
Taking the reciprocal, we find: Rt = 12/13 ohms

Combining series and parallel resistances

Complex circuits can have both series and parallel resistances
To simplify the analysis, we can use the concept of equivalent resistance
Equivalent resistance is a single resistor that can replace a combination of resistors in a circuit, preserving the same current-voltage relationship
In a series-parallel circuit, we start by finding the equivalent resistance of series resistors and then replace parallel resistors with their equivalent resistance
The final equivalent resistance is then the total resistance of the circuit

Example: Combining series and parallel resistances

Let’s consider a circuit with two series resistors connected in parallel with another resistor
R1 = 2 ohms, R2 = 3 ohms, and R3 = 4 ohms
First, calculate the equivalent resistance of the series resistors: R12 = R1 + R2 = 2 + 3 = 5 ohms
Then, calculate the equivalent resistance of the parallel resistors: 1/Rt = 1/R12 + 1/R3 = 1/5 + 1/4 = 9/20
Taking the reciprocal, we find: Rt = 20/9 ohms

Electrical power and energy

Power is the rate at which work is done or energy is transferred
In electrical circuits, power is calculated using the equation: P = VI, where P is power (in watts), V is voltage (in volts), and I is current (in amperes)
Energy is the amount of work done or transferred
Electric energy is the product of power and time: E = Pt, where E is energy (in joules), P is power (in watts), and t is time (in seconds)
Kilowatt-hour (kWh) is a commonly used unit of energy, equal to 1 kilowatt of power consumed in 1 hour

Example: Calculating power and energy

Consider a device with a voltage of 220V and a current of 5A
Using the power equation, we can calculate the power: P = 220 * 5 = 1100W
If the device operates for 2 hours, we can calculate the energy consumed using the energy equation: E = Pt = 1100 * 2 = 2200J or 2.2kWh

Electric current and its effects

Electric current is the flow of electric charge through a conductor
It is measured in amperes (A)
When a current flows through a conductor, it produces several effects, including heating, magnetic field generation, and chemical reactions
The heating effect is utilized in appliances like electric heaters
The magnetic field effect is utilized in electromagnets and electric motors
The chemical effect is utilized in electroplating and electrolysis processes

Superconductivity

Superconductivity is a phenomenon in which certain materials can conduct electric current with zero resistance
Superconductors exhibit unique properties at very low temperatures
Superconducting materials have no electrical resistance, allowing for lossless transmission of electricity
Superconductors are used in various applications, including medical imaging, particle accelerators, and power transmission lines

Electromotive force and Ohm’s law - Current and Electricity - Change in resistance due to increase in temperature

Application of Ohm’s law in circuits

Ohm’s law is widely used in electrical circuits for analysis and calculations
It helps determine the current flowing through a circuit, the voltage across each component, and the power dissipated
By manipulating the equation V = IR, we can solve various circuit problems
Ohm’s law is applicable to both DC (direct current) and AC (alternating current) circuits
It provides a fundamental understanding of the relationship between voltage, current, and resistance

Example: Applying Ohm’s law in a circuit

Let’s consider a circuit with a resistor of 10 ohms and a current of 2 amperes
Using Ohm’s law, we can calculate the voltage across the resistor: V = IR = 2 * 10 = 20 volts
Similarly, if the voltage across a component is known, Ohm’s law can help calculate the current or resistance

Resistivity and Conductivity

Resistivity (ρ) is a fundamental property of a material that quantifies its resistance to electric current
It depends on the nature and structure of the material
Conductivity (σ) is the reciprocal of resistivity and is a measure of a material’s ability to conduct electric current
Conductivity is commonly used in electrical engineering and is measured in units of Siemens per meter (S/m)
Different materials have different resistivities and conductivities

Temperature coefficient of resistance

The temperature coefficient of resistance (α) quantifies the change in resistance with temperature
It is defined as the change in resistance per degree Celsius (Ω/°C)
The temperature coefficient is positive for most conductors, indicating that resistance increases with temperature
However, there are also materials with negative temperature coefficients, such as thermistors
The temperature coefficient is an important parameter for understanding and designing circuits

Calculation of resistance change with temperature

To calculate the change in resistance due to temperature, we use the formula: ΔR = R₀ * α * ΔT
ΔR is the change in resistance, R₀ is the initial resistance at temperature T₀, α is the temperature coefficient of resistance, and ΔT is the change in temperature
By knowing the temperature coefficient of a material and the initial resistance at a given temperature, we can estimate the resistance at a different temperature

Example: Resistance change with temperature

Let’s consider a wire with an initial resistance of 20 ohms at 25°C
The temperature coefficient of resistance for this wire is 0.004 Ω/°C
If the temperature increases to 50°C, we can calculate the change in resistance using the formula: ΔR = R₀ * α * ΔT
ΔR = 20 * 0.004 * (50 - 25) = 2 ohms
Therefore, the new resistance at 50°C is 20 + 2 = 22 ohms

Factors affecting resistance

Resistance can be influenced by various factors other than temperature
Length: Longer conductors have higher resistance, as electrons have to travel a greater distance
Cross-sectional area: Wider conductors have lower resistance, as there is more space for electron flow
Material: Different materials have different resistivities, resulting in different resistances even with the same dimensions
Temperature: As discussed earlier, resistance generally increases with an increase in temperature

Power dissipation in resistive elements

When electric current flows through a resistor, it dissipates power in the form of heat
The power dissipated by a resistor can be calculated using the formula: P = I^2R or P = V^2/R
P is the power in watts, I is the current in amperes, V is the voltage across the resistor, and R is the resistance
This equation demonstrates the relationship between power, current, voltage, and resistance

Example: Power dissipation in a resistor

Let’s consider a circuit with a voltage of 12V and a resistance of 4 ohms
We can calculate the power dissipated using the formula P = V^2/R: P = 12^2 / 4 = 36 watts
Similarly, if the current through the resistor is known, we can use P = I^2R to calculate the power

Summary and key points

Electromotive force (EMF) is the energy provided per unit charge by a source like a battery or generator
Ohm’s law relates the current, voltage, and resistance in a circuit
Resistance can change with temperature due to the temperature coefficient of resistance
Ohm’s law and the concept of resistance are fundamental in circuit analysis
Factors such as length, cross-sectional area, material, and temperature affect resistance
Power dissipation in a resistor can be calculated using the equations P = I^2R and P = V^2/R
Understanding these principles is crucial for understanding and designing electrical circuits