What causes the random motion of electrons in a conductor?

The random motion of electrons in a conductor is caused by collisions between free electrons and the ions within the material.

What is the role of resistance in the LC circuit producing LC oscillations?

In an LC circuit, resistance opposes the flow of current. As current passes through the inductor during capacitor discharge, energy is lost as heat, causing the amplitude of the oscillations to decrease. This results in damped oscillations, a characteristic of resistance in the LC circuit.

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Difference Between Resistance and Impedance

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Difference Between Resistance And Impedance

In electrical and electronic engineering, grasping the difference between resistance and impedance is essential for circuit analysis and design. Resistance measures the opposition to direct current (DC) flow, quantified in ohms (Ω), and is a purely real quantity that does not vary with frequency. It is typically associated with resistors, which dissipate electrical energy as heat. Conversely, Impedance broadens the concept of resistance to alternating current (AC) circuits. It combines resistance with the effects of inductance and capacitance, resulting in a complex quantity that accounts for both magnitude and phase difference between voltage and current. Measured in ohms, impedance is vital for understanding AC circuit behavior under different conditions.

1.0Definition of Resistance

It is the opposition offered to the flow of electric charge in the conductor. It is defined as the ratio of the potential difference across the ends of the conductor to the current flowing through it.

$R = \frac{V}{I}$

SI Unit of Resistance is Ohm $Ω$
Resistance of a conductor is said to be 1 $Ω$ , if current of 1A flows through it, when potential difference of 1V is applied across it.
Dimensional Formula: $[M L^{2} T^{- 3} A^{- 2}]$
Resistance of a conductor can be measured with the help of an instrument known as Ohmmeter.

2.0Cause Of Resistance

Resistance is the opposition a conductor presents to the flow of electric charge. When a conductor is connected to a cell or battery, free electrons move from the negative to the positive terminal, generating an electric current. As these electrons travel, they collide with ions in the conductor, which creates resistance to their flow.
Electrical resistance is influenced by the material's properties, ion arrangement, length, thickness, and temperature.

3.0Factors Affecting Resistance

Resistance of a conductor depends upon:

Nature of Material of the conductor
Dimensions-Length and Area of Cross-section

Length-Resistance (R) of a conductor is directly proportional to its length (l)

$\to$ more the length, of a conductor, more is its resistance

Area-of the cross-section-The resistance of a conductor is inversely proportional to its area of cross-section.

Smaller the thickness of a conductor, more is its resistance

Temperature-Resistance also depends upon the temperature of the conductor. If temperature of a conductor increases, its resistance also increases or vice-versa

R ∝ (l/A) $\Rightarrow$ R= $ρ$ l/A =Resistivity of the material

4.0Definition Of Impedance (Z)

The total effective opposition offered by LCR circuit to alternating current is known as Impedance. Impedance comprises of three parts Resistance (R), Inductive Reactance (XL), Capacitive Reactance $(X_{C})$ . Where $X_{L} an d X_{C}$ are opposite to each other.
In series LCR Circuit, the total reactance is $\mp (X_{L} - X_{C})$
Reciprocal of Reactance is known as susceptance
Unit of Impedance is Ohm $(Ω)$
Reciprocal of Impedance is called Admittance (A) $A = \frac{1}{Z}$
Unit of Admittance is Siemen, mho, $ohm^{- 1}$

Phasor Diagram Of Series LCR Circuit

Potential Difference across inductor, $V_{L} = I X_{L}$ (Voltage leads current I by an angle of $\frac{π}{2}$ )
Potential Difference across capacitor, $V_{C} = I X_{C}$ (Voltage lags behind the current I by an angle of $\frac{π}{2}$ )
Potential Difference across resistor, $V_{R} = I R$ (Voltage is in phase with current)
Resultant of $V_{R}$ and $(V_{L} - V_{c})$ is given by OP, magnitude of OP is given by,

$OP = (O A)^{2} + (OB)^{2} = (V_{R})^{2} + (V_{L} - V_{C})^{2}$

$V = V_{R}^{2} + (V_{L} - V_{C})^{2}$

$V = I^{2} R^{2} + (I X_{L} - I X_{C})^{2}$

$V = I R^{2} + (X_{L} - X_{C})^{2}$

$\frac{V}{I} = R^{2} + (X_{L} - X_{C})^{2} ∴ \frac{V}{I} = Z$

$Z = R^{2} + (X_{L} - X_{C})^{2}$ , it is the effective opposition offered by series LCR circuit called impedance of the circuit

Total Current in the circuit,

$I = \frac{V}{Z} = \frac{V}{R ^{2} + ( X _{L} - X _{c} ) ^{2}}$

If $ϕ$ is the phase angle between V and I,

$Tan ϕ = \frac{V _{L} - V _{C}}{V _{R}} = \frac{I X _{L} - I X _{C}}{I R} = \frac{X _{L} - X _{C}}{R}$

5.0Impedance Triangle

$Z = R^{2} + (X_{L} - X_{C})^{2}$
$Z = R^{2} + X_{L}^{2}$
$Z = R^{2} + X_{C}^{2}$

6.0Sample Questions on Difference Between Resistance And Impedance

Q-1.Distinguish between Resistance and Impedance?

Solution:

Resistance	Impedance
It is the opposition offered by the resistor to the flow of current.	It is the effective opposition offered by the combination of resistor,inductor and capacitor.
It is independent of the frequency of the source of the current.	It depends on the frequency of the source of current.

Q-2.A resistor $30Ω$ , inductor of reactance $10Ω$ and capacitor of reactance $10Ω$ are connected in series to an a.c voltage source $V = V_{0} 3002 Sin ω t$ . Calculate the current in the circuit.

Solution:

$I = \frac{V}{Z} = \frac{V}{R ^{2} + ( X _{L} - X _{c} ) ^{2}} = \frac{V}{R ^{2} + ( X _{L} - X _{c} ) ^{2}} = \frac{V _{0}}{2 R} = \frac{300 2}{2 \times 30} = 10 A (X_{L} = X_{C}, Circuit becomes Resistive)$

Q-3. Draw a graph illustrating how the resistance of a conducting wire varies with its radius, while keeping the wire's length and temperature constant.

Solution: $R = ρ \frac{l}{A} = \frac{ρl}{π r ^{2}}$ Since and l are constant $R \propto \frac{1}{r ^{2}}$ Variation of R with r

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Difference Between Resistance And Impedance

In electrical and electronic engineering, grasping the difference between resistance and impedance is essential for circuit analysis and design. Resistance measures the opposition to direct current (DC) flow, quantified in ohms (Ω), and is a purely real quantity that does not vary with frequency. It is typically associated with resistors, which dissipate electrical energy as heat. Conversely, Impedance broadens the concept of resistance to alternating current (AC) circuits. It combines resistance with the effects of inductance and capacitance, resulting in a complex quantity that accounts for both magnitude and phase difference between voltage and current. Measured in ohms, impedance is vital for understanding AC circuit behavior under different conditions.

1.0Definition of Resistance

It is the opposition offered to the flow of electric charge in the conductor. It is defined as the ratio of the potential difference across the ends of the conductor to the current flowing through it.

$R = \frac{V}{I}$

SI Unit of Resistance is Ohm $Ω$
Resistance of a conductor is said to be 1 $Ω$ , if current of 1A flows through it, when potential difference of 1V is applied across it.
Dimensional Formula: $[M L^{2} T^{- 3} A^{- 2}]$
Resistance of a conductor can be measured with the help of an instrument known as Ohmmeter.

2.0Cause Of Resistance

Resistance is the opposition a conductor presents to the flow of electric charge. When a conductor is connected to a cell or battery, free electrons move from the negative to the positive terminal, generating an electric current. As these electrons travel, they collide with ions in the conductor, which creates resistance to their flow.
Electrical resistance is influenced by the material's properties, ion arrangement, length, thickness, and temperature.

3.0Factors Affecting Resistance

Resistance of a conductor depends upon:

Nature of Material of the conductor
Dimensions-Length and Area of Cross-section

Length-Resistance (R) of a conductor is directly proportional to its length (l)

$\to$ more the length, of a conductor, more is its resistance

Area-of the cross-section-The resistance of a conductor is inversely proportional to its area of cross-section.

Smaller the thickness of a conductor, more is its resistance

Temperature-Resistance also depends upon the temperature of the conductor. If temperature of a conductor increases, its resistance also increases or vice-versa

R ∝ (l/A) $\Rightarrow$ R= $ρ$ l/A =Resistivity of the material

4.0Definition Of Impedance (Z)

The total effective opposition offered by LCR circuit to alternating current is known as Impedance. Impedance comprises of three parts Resistance (R), Inductive Reactance (XL), Capacitive Reactance $(X_{C})$ . Where $X_{L} an d X_{C}$ are opposite to each other.
In series LCR Circuit, the total reactance is $\mp (X_{L} - X_{C})$
Reciprocal of Reactance is known as susceptance
Unit of Impedance is Ohm $(Ω)$
Reciprocal of Impedance is called Admittance (A) $A = \frac{1}{Z}$
Unit of Admittance is Siemen, mho, $ohm^{- 1}$

Phasor Diagram Of Series LCR Circuit

Potential Difference across inductor, $V_{L} = I X_{L}$ (Voltage leads current I by an angle of $\frac{π}{2}$ )
Potential Difference across capacitor, $V_{C} = I X_{C}$ (Voltage lags behind the current I by an angle of $\frac{π}{2}$ )
Potential Difference across resistor, $V_{R} = I R$ (Voltage is in phase with current)
Resultant of $V_{R}$ and $(V_{L} - V_{c})$ is given by OP, magnitude of OP is given by,

$OP = (O A)^{2} + (OB)^{2} = (V_{R})^{2} + (V_{L} - V_{C})^{2}$

$V = V_{R}^{2} + (V_{L} - V_{C})^{2}$

$V = I^{2} R^{2} + (I X_{L} - I X_{C})^{2}$

$V = I R^{2} + (X_{L} - X_{C})^{2}$

$\frac{V}{I} = R^{2} + (X_{L} - X_{C})^{2} ∴ \frac{V}{I} = Z$

$Z = R^{2} + (X_{L} - X_{C})^{2}$ , it is the effective opposition offered by series LCR circuit called impedance of the circuit

Total Current in the circuit,

$I = \frac{V}{Z} = \frac{V}{R ^{2} + ( X _{L} - X _{c} ) ^{2}}$

If $ϕ$ is the phase angle between V and I,

$Tan ϕ = \frac{V _{L} - V _{C}}{V _{R}} = \frac{I X _{L} - I X _{C}}{I R} = \frac{X _{L} - X _{C}}{R}$

5.0Impedance Triangle

$Z = R^{2} + (X_{L} - X_{C})^{2}$
$Z = R^{2} + X_{L}^{2}$
$Z = R^{2} + X_{C}^{2}$

6.0Sample Questions on Difference Between Resistance And Impedance

Q-1.Distinguish between Resistance and Impedance?

Solution:

Resistance	Impedance
It is the opposition offered by the resistor to the flow of current.	It is the effective opposition offered by the combination of resistor,inductor and capacitor.
It is independent of the frequency of the source of the current.	It depends on the frequency of the source of current.

Q-2.A resistor $30Ω$ , inductor of reactance $10Ω$ and capacitor of reactance $10Ω$ are connected in series to an a.c voltage source $V = V_{0} 3002 Sin ω t$ . Calculate the current in the circuit.

Solution:

$I = \frac{V}{Z} = \frac{V}{R ^{2} + ( X _{L} - X _{c} ) ^{2}} = \frac{V}{R ^{2} + ( X _{L} - X _{c} ) ^{2}} = \frac{V _{0}}{2 R} = \frac{300 2}{2 \times 30} = 10 A (X_{L} = X_{C}, Circuit becomes Resistive)$

Q-3. Draw a graph illustrating how the resistance of a conducting wire varies with its radius, while keeping the wire's length and temperature constant.

Solution: $R = ρ \frac{l}{A} = \frac{ρl}{π r ^{2}}$ Since and l are constant $R \propto \frac{1}{r ^{2}}$ Variation of R with r

Frequently Asked Questions

What causes the random motion of electrons in a conductor?

What is the role of resistance in the LC circuit producing LC oscillations?

Frequently Asked Questions

What causes the random motion of electrons in a conductor?

What is the role of resistance in the LC circuit producing LC oscillations?

Join ALLEN!

Difference Between Resistance And Impedance

1.0Definition of Resistance

2.0Cause Of Resistance

3.0Factors Affecting Resistance

4.0Definition Of Impedance (Z)

Phasor Diagram Of Series LCR Circuit

5.0Impedance Triangle

6.0Sample Questions on Difference Between Resistance And Impedance

Table of Contents

Join ALLEN!

Difference Between Resistance And Impedance

1.0Definition of Resistance

2.0Cause Of Resistance

3.0Factors Affecting Resistance

4.0Definition Of Impedance (Z)

Phasor Diagram Of Series LCR Circuit

5.0Impedance Triangle

6.0Sample Questions on Difference Between Resistance And Impedance

Table of Contents