Electrical Resistance – Explanation

What is resistance?

Resistance is the property of a material that restricts the movement of electrons.

When a potential difference is applied across a conductor, an electric field is created throughout the circuit, causing the free electrons to drift or move and collide with the metal particles. The more impact that the electrons in a conductor endure, the more resistance the conductor presents.

What is the reason for resistance?

The primary cause of  resistance is the collision of electrons with the metal particles of the conduit they travel through. When these electrons collide, active energy is transferred, the electrons slow down, and obstruction results.

Measuring the Resistance of a wire using Ohm’s law

You can measure the resistance of a wire using a simple experiment:Connect the wire to a circuit with a known voltage source and an ammeter.
Measure the current flowing through the wire.
Apply Ohm’s Law: R=VI  R = V/I   

Electrical Conductance: Detailed Explanation

Electrical Conductance is a measure of how easily electric current flows through a material. It is represented by the letter G and is the reciprocal of electrical resistance(R). The siemens (S), which is equal to A/V (amperes per volt), is the unit of conductance.

Electrical Conductance: Key Concepts

Ohm’s Law: Conductance is derived from Ohm’s Law, which states:

V = IR     where:

V= Voltage (in volts, V),

I = Current (in amperes, A),

R = Resistance (in ohms, Ω).

Conductance G is the inverse of resistance:

G=1/R

Relationship with Current and Voltage:

 I = GV

 This shows that current is directly proportional to conductance and voltage.

Factors Influencing Conductance

Material:

Insulators, like rubber, have low conductance, whereas conductors, like metals, have high conductance.

Temperature:

As the temperature rises, conductance for the majority of conductors falls.

Cross-sectional area:

The greater the material’s cross-sectional area, the higher its conductance.

Length:

As a material’s length increases, conductance falls.

Conductivity (σ)

Conductance is related to conductivity σ by the formula:

G=A/ρL   or   G= σA/L

A = Cross-sectional area of the material,

L = Length of the material.

Electrical Conductance :Practice Numerical Problems-1

S.No.	Problem	Apply the  formula	Answer
1.	A copper wire has a resistance of 0.5 Ω. What is its conductance?	G=1/R	?
2.	The conductance of a resistor is 0.25 S. Find its resistance.	R=1/G	?
3.	A resistor has a conductance of 0.2 S. What is its resistance?	R=1/G	?
4.	The resistance of a nichrome wire is 15 Ω. What is its conductance?	G=1/R	?
5.	A wire has a resistance of 10 Ω .Calculate its conductance	G=1/R	?

Electrical Conductance :Practice Numerical Problems-2

S.No.	Problem	Apply the  formula	Answer
1.	Two resistors of 6 Ω and 3 Ω are connected in parallel. Find the total conductance.	G=1/Rp	?
2.	A circuit has a conductance of 2 S and a voltage of 20 V applied across it. Calculate the current flowing through the circuit.	I=V×G	?
3.	A material has a resistance of 20 Ω  . If its length is doubled and cross-sectional area is halved, what will be its new conductance?	G=1/R’	?
4.	A wire carries a current of 5 A when a voltage of 10 V is applied. Calculate its conductance.	G=I/V	?
5.	A conductor has a resistance of  5 Ω.. If its conductance is doubled, what will be its new resistance?	R=1/G	?

Electrical Conductance:Practice Numerical Problems-3

S.No.	Problem	Apply the  formula	Answer
1.	A conductor has a conductance of 0.01 S. If the voltage across it is  100 V, find the current.	I = GV	?
2.	A wire has a conductance of 0.5 S. If the voltage across it is 12 V, calculate the power dissipated.	I=GV     P=VI	?
3.	A wire has a conductance of 0.1 S. If the current flowing through it is 0.5 A, what is the voltage across it?	V=I/G	?
4.	A wire carries a current of 5 A when a voltage of 10 V is applied. Calculate its conductance.	G=I/V	?
5.	A material has a conductance of  2 S. If a voltage of 5 V is applied, calculate the current flowing through it.	I = GV	?

Electrical Conductance:Practice Numerical Problems-4

S.No.	Problem	Apply the  formula	Answer
1.	The length of a copper wire is 2 m, and its cross-sectional area is 1×10-6 m2. The resistivity of copper is 1.68×10−8 Ω⋅m. Calculate its conductance.	G=A/ρL	?
2.	A silver wire of length 0.5 m and cross-sectional area 2×10−6 m2 has a resistivity of 1.59×10−8  Ω⋅m. Calculate its conductance.	G=A/ρL	?
3.	A wire of resistivity 2.0×10−7 Ω⋅m has a length of 3 m and a cross-sectional area 0f 1.5×10−6 m2. Calculate its conductance.	G=A/ρL	?
4.	A wire of length of 2 m and cross-sectional area 1 x 10-6 m2 has a conductivity of  5.8×10-7  S/m. Calculate its conductance.	G=σA/l	?
5.	Two conductors have resistances of 4 Ω and 8 Ω, connected in parallel. Calculate the total conductance.	G=1/Rp	?

Electrical Conductance : Answers for practice numerical problems-1

S. No.1	S. No.2	S. No.3	S. No.4	S. No.5
2 S	4 Ω	5 Ω	0.067 S	0.1 S

Electrical Conductance : Answers for practice numerical problems-2

S. No.1	S. No.2	S. No.3	S. No.4	S. No.5
0.5 S	40 A	0.0125	0.5 S	2.5 Ω.

Electrical Conductance : Answers for practice numerical problems-3

S. No.1	S. No.2	S. No.3	S. No.4	S. No.5
1 A	72 W	5 V	0.5 S	10 A

Electrical Conductance : Answers for practice numerical problems-4

S. No.1	S. No.2	S. No.3	S. No.4	S. No.5
29.76 S	251.57 S	2.5 S	29 S	0.375 S

Factors influence Electrical Resistance and Conductance

The electrical resistance and conductance of a material depend on several key factors:

1. Material Composition: Different materials have varying levels of electrical resistance and conductance. For example, metals like copper and silver are excellent conductors, while materials like rubber and glass are insulators.
2. Temperature: The resistance of most materials changes with temperature. For conductors, resistance typically increases with an increase in temperature. For semiconductors, resistance decreases as temperature rises.
3. Length of the Conductor: The longer the conductor, the higher the resistance. This is because electrons have to travel a longer distance, which increases the chances of collisions with atoms in the material.
4. Cross-Sectional Area: A conductor with a larger cross-sectional area has a lower resistance compared to one with a smaller area. This is because a larger area allows more electrons to flow through simultaneously.
5. Type of Material: The intrinsic properties of the material, such as the number of free electrons available for conduction, significantly influence resistance and conductance.
6. Impurities in the Material: The presence of impurities can disrupt the regular arrangement of atoms and increase the resistance. Pure materials tend to have lower resistance compared to impure ones.
7. Magnetic Fields: For some materials, the presence of a magnetic field can affect resistance. This is particularly true for materials exhibiting the Hall effect or magnetoresistance.
8. Frequency of the Applied Voltage: In AC circuits, the frequency of the applied voltage can influence the effective resistance (or impedance) of a material.

These factors play crucial roles in determining how easily an electric current can flow through a material.

Significance of Electrical Resistance and conductance in Electrical Circuits:

The significance of electrical resistance and conductance in electrical circuits cannot be overstated, as they are foundational concepts that influence how circuits function:

1. Control of Current Flow: Resistance controls the amount of current flowing through a circuit. By adjusting the resistance, you can regulate the current to desired levels, which is essential for the safe and efficient operation of electrical devices.
2. Energy Dissipation: Resistance is responsible for converting electrical energy into heat. This principle is harnessed in devices like electric heaters and incandescent light bulbs, where the heat generated by resistance is the intended output.
3. Voltage Drop: In a circuit, resistance causes a drop in voltage across components. Understanding and calculating voltage drops is crucial for designing circuits to ensure that components receive the appropriate voltage for proper operation.
4. Power Consumption: Resistance affects the power consumed by a circuit or device. The power consumed (P) is given by the formula P=I2⋅RP = I^2 R, where II is the current and RR is the resistance. This is important for energy efficiency and for designing power supplies.
5. Signal Integrity: In high-frequency circuits, such as those used in telecommunications, the resistance of the components and wiring can affect signal integrity. Minimizing resistance in these circuits is crucial to maintain signal quality.
6. Circuit Protection: Resistors can be used to protect sensitive components by limiting the current that flows through them. They are often used in conjunction with fuses and circuit breakers to prevent damage from excessive current.
7. Temperature Effects: Resistance varies with temperature, and this property is used in devices like thermistors to measure temperature changes accurately. Conductance, the reciprocal of resistance, is also significant in such applications.
8. Impedance Matching: In AC circuits, the concept of impedance, which includes resistance, is vital for matching components to ensure maximum power transfer and reduce signal reflections.

Understanding the interplay between resistance and conductance helps in the effective design, analysis, and troubleshooting of electrical and electronic circuits, ensuring they operate safely, efficiently, and reliably.

Conclusion:

In conclusion, electrical resistance and conductance are fundamental concepts that significantly influence the behavior of electrical circuits. These properties are determined by various factors, including material composition, temperature, length, cross-sectional area, impurities, magnetic fields, and frequency of the applied voltage. Understanding these factors allows for effective control and regulation of current flow, energy dissipation, voltage drops, and power consumption in circuits.

The significance of resistance and conductance extends to practical applications such as circuit protection, signal integrity, impedance matching, and temperature measurement. By grasping the principles of resistance and conductance, engineers and technicians can design, analyze, and troubleshoot electrical and electronic systems to ensure their safe, efficient, and reliable operation.

Overall, a thorough understanding of these concepts is essential for anyone working with electrical circuits, as it enables the optimization and improvement of various electrical and electronic devices and systems.