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$\mathrm{\Omega }$
• Resistance of a conductor is said to be 1$\Omega$, 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:

1. Nature of Material of the conductor
2. 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

3. 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= $\rho$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 $X_{L}and{X}_C$ are opposite to each other.
• In series LCR Circuit, the total reactance is $\mp \left(X_L-X_C\right)$
• Reciprocal of Reactance is known as susceptance
• Unit of Impedance is Ohm $(\Omega )$
• Reciprocal of Impedance is called Admittance (A)$A=\frac{1}{Z}$
• Unit of Admittance is Siemen, mho,${\text{ ohm }}^{-1}$

Phasor Diagram Of Series LCR Circuit

• Potential Difference across inductor, $V_L=I{X}_L$(Voltage leads current I by an angle of $\frac{\pi }{2}$)
• Potential Difference across capacitor, $V_C=I{X}_C$  (Voltage lags behind the  current I by an angle of $\frac{\pi }{2}$)
• Potential Difference across resistor, $V_R=IR$ (Voltage is in phase with current)
• Resultant of $V_R$ and $\left(V_L-V_c\right)$ is given by OP, magnitude of OP is given by,

$OP=\sqrt{(OA{)}^2+(OB{)}^2}=\sqrt{{\left(V_R\right)}^2+{\left(V_L-V_C\right)}^2}$

$V=\sqrt{V_R^2+{\left(V_L-V_C\right)}^2}$

$V=\sqrt{I^2{R}^2+{\left(I{X}_L-I{X}_C\right)}^2}$

$V=I\sqrt{R^2+{\left(X_L-X_C\right)}^2}$

$\frac{V}{I}=\sqrt{R^2+{\left(X_L-X_C\right)}^2}\therefore \frac{V}{I}=Z$

$Z=\sqrt{R^2+{\left(X_L-X_C\right)}^2}$, it is the effective opposition offered by series LCR circuit called impedance of the circuit

• Total Current in the circuit,

$I=\frac{V}{Z}=\frac{V}{R^2+{\left(X_L-X_c\right)}^2}$

• If $\varphi$ is the phase angle between V and I,

$\mathrm{Tan}\varphi =\frac{V_L-V_C}{V_R}=\frac{I{X}_L-I{X}_C}{IR}=\frac{X_L-X_C}{R}$

5.0Impedance Triangle

• $Z=\sqrt{R^2+{\left(X_L-X_C\right)}^2}$
• $Z=\sqrt{R^2+X_L^2}$
• $Z=\sqrt{R^2+X_C^2}$

6.0Sample Questions on Difference Between Resistance And Impedance

Q-1.Distinguish between Resistance and Impedance?

Solution:

Q-2.A resistor $30\Omega$, inductor of reactance $10\Omega$ and capacitor of reactance $10\Omega$ are connected in series to an a.c voltage source $V=V_{0}300\sqrt{2}\mathrm{Sin}\omega t$. Calculate the current in the circuit.

Solution:

$I=\frac{V}{Z}=\frac{V}{R^2+{\left(X_L-X_c\right)}^2}=\frac{V}{R^2+{\left(X_L-X_c\right)}^2}=\frac{V_0}{\sqrt{2}R}=\frac{300\sqrt{2}}{\sqrt{2}\times 30}=10\mathrm{A}\left(X_L=X_C,\text{ Circuit becomes Resistive }\right)$

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.