Equivalent Resistance Formula: Series And Parallel Circuit Example

Education Journalist | Study Abroad Lead

Equivalent Resistance formula of an object is the measure of how much it opposes the flow of current. It is calculated in ohms. The amount of opposition to the flow of current can be increased by combining two or more resistances in a series or parallel arrangement.

Table of Content

What is Equivalent Resistance?
Series Arrangement of Resistances
Parallel Arrangement of Resistances
Things to Remember
Previous Year Questions
Sample Questions

Key Terms: Equivalent Resistance, Equivalent Resistance Calculator, Formula of Equivalent Resistance, Equivalent Resistance Formula in Parallel, Equivalent Resistance in Series

What is Equivalent Resistance?

[Click Here for Sample Questions]

Equivalent Resistance refers to the point where the total resistance of a series or parallel arrangement is calculated. There are separate formulae to calculate equivalent resistance for series and parallel arrangements respectively.

Either the whole circuit or in a part of the circuit.
Equivalent resistance is defined between nodes or two terminals of the network.
Single resistor can substitute the complete network for a specified voltage and the current can be obtained when used as a network.
If a lot of energy is required then the resistance necessary will also be high. The equivalent resistance of a network is a single resistor which can replace the entire network.
The applied voltage (V) will be the same as current (I).

Equivalent Resistance

Equivalent Resistance

Discover about the Chapter video:

Current Electricity Detailed Video Explanation:

Also Check:

Content Related To Resistors In Parallel Formula
Relation Between Power And Resistance	Derivation Of Drift Velocity	Difference Between Emf And Voltage
Internal Resistance Formula	Difference Between Air Conditioning And Refrigeration	Helical Motion Of Charged
Power Of Alternating Current	Differences Between Acceleration And Velocity	Types Of Current
Unit Of Resistance	Difference Between Ac And Dc	Uses Of Transformer
Difference Between Ammeter And Voltmeter	Resistivity Temperature Dependence	Electric Current Formula
Uses Of Resistor	Current Density Formula	Resistivity Formula
Permeability	Difference Between Electric	Relation Between Resistance And Length
Resistance Formula	Field And Magnetic Field	Kirchoff's Voltage Law

Series Arrangement of Resistance

[Click Here for Previous Year Questions]

Series Arrangement refers to the arrangement of resistors in which all the resistors are connected in one line. The total resistance of such an arrangement is the sum of each resistance.

R_S = R₁ + R₂ + R₃ + …….

The series arrangement of resistors is implied to improve/increase the total resistance.

Resistance formula for series arrangement

Example: Two 6-Ω resistors are connected in series, they are equivalent to having one 12-Ω resistor in the circuit. This is the concept of equivalent resistance in a series circuit.

Example of Series Arrangement of Resistance

Example of Series Arrangement of Resistance

Parallel Arrangement of Resistance

[Click Here for Sample Questions]

Parallel Arrangement refers to the arrangement of resistors in which all the resistors are connected parallel to each other. The reciprocal of the total resistance of such an arrangement is the sum of the reciprocal of each resistance.

1 / R_P = 1 / R₁ + 1 / R₂ + 1 / R₃ + …….

The parallel arrangement of resistors is implied to decrease the total resistance.

Resistance formula for Parallel Resistance

Example: Two resistors positioned in parallel branches, both of them have the same resistance value of 4. The circuit has two equivalent paths for the charge transport but, just one-half of the charge can choose to travel through the branch.

Parallel Arrangement of Resistance

Parallel Arrangement of Resistance

The branch gives 4Ω of resistance to any charge flowing through it and only ½ of all the charge flowing through the circuit may meet 4Ω of resistance of that branch. Hence, the presence of two 4Ω resistors in parallel will be equal to one 2Ω resistor in the circuit.This is the concept of equivalent resistance in a parallel circuit.

Also Check:

Chapter Related Topic
Unit Of Voltage	Drift Velocity	Unit Of Specific Resistance
Electrical Resistance	Electric Current	Wheatstone Bridge
Cells, Emf, Internal Resistance	Combination Of Resistors-Series And Parallel	Potentiometer
Unit Of Current	Power Transformers	Circuit Diagram
Static Electricity	Current Electricity	Electromotive Force
Cells In Series And In Parallel	Class 12 Physics Chapter 3 Current Electricity	Ampere
Network Analysis	Current Density	Current Density Formula
Electrical Current	Ohm’s Law And Its Limitations	Resistor Colour Codes
Meter Bridge	Types Of Resistors	Voltage Divider Formula

Things to Remember

The resistance of an object is the measure of how much it opposes the flow of current. It is calculated in ohms.
Equivalent Resistance refers to the point where the total resistance of a series or parallel arrangement is calculated.
Series Arrangement refers to the arrangement of resistors in which all the resistors are connected in one line.
The total resistance of the series arrangement is the sum of each resistance.
Parallel Arrangement refers to the arrangement of resistors in which all the resistors are connected parallel to each other.
The series arrangement of resistors is implied to improve/increase the total resistance.
The parallel arrangement of resistors is implied to decrease the total resistance.

Previous Year Questions

Sample Questions

Ques 1. What is the resistance of an object? (2 marks)

Ans. The resistance of an object is the measure of how much it opposes the flow of current. It is calculated in ohms. The amount of opposition to the flow of current can be increased by combining two or more resistances in a series or parallel arrangement.

Ques 2. What is Equivalent Resistance? (2 marks)

Ans. Equivalent Resistance refers to the point where the total resistance of a series or parallel arrangement is calculated. There are separate formulae to calculate equivalent resistance for series and parallel arrangements respectively.

Ques 3. What is the Series Arrangement of Resistances? (2 marks)

Ans. Series Arrangement refers to the arrangement of resistors in which all the resistors are connected in one line. The total resistance of such an arrangement is the sum of each resistance.

R_S = R₁ + R₂ + R₃ + …….

The series arrangement of resistors is implied to improve/increase the total resistance.

Ques 4. What is the Parallel Arrangement of Resistances? (2 marks)

Ans. Parallel Arrangement refers to the arrangement of resistors in which all the resistors are connected parallel to each other. The reciprocal of the total resistance of such an arrangement is the sum of the reciprocal of each resistance.

1 / R_P = 1 / R₁ + 1 / R₂ + 1 / R₃ + …….

The parallel arrangement of resistors is implied to decrease the total resistance.

Ques 5. Find the equivalent resistance for a circuit where R1 = 15â„¦, R2 20â„¦, and R3 = 30â„¦ are in a series arrangement. (2 marks)

Ans. For a series arrangement of resistors, the equivalent resistance is:

R_S = R₁ + R₂ + R₃

R_S = 15â„¦ + 20â„¦ + 30â„¦

R_S = 65â„¦

Ques 6. Find the equivalent resistance for a circuit where R1 = 15â„¦, R2 20â„¦, and R3 = 30â„¦ are in a parallel arrangement. (3 marks)

Ans. For a parallel arrangement of resistors, the equivalent resistance is:

1 / R_P = 1 / R₁ + 1 / R₂ + 1 / R₃

1 / R_P = 1 / 15â„¦ + 1 / 20â„¦ + 1 / 30â„¦

1 / R_P = (4 + 3 + 2) / 60â„¦

1 / R_P = 9 / 60â„¦

1 / R_P = 3 / 20â„¦

R_P = 20 / 3â„¦

Ques 7. What is the equivalent resistance if 3Ω, 20Ω and 32Ω are connected in series. (2 marks)

Ans. Equivalent resistance in series is given by

R = R₁ + R₂ + …… + R_n

= 3 Ω + 20 Ω + 32 Ω

Ques 8. What is the equivalent resistance if 34 Ω and 20 Ω are connected in parallel. (3 marks)

Ans. Equivalent resistance in parallel is given by

1/R_P= 1/R₁ + 1/R₂ + 1/R₃+.......+ 1/R_n

1/R_P= \(\frac{1}{34} + \frac{1}{20}\)

= 0.029 + 0.05

= 0.079

R_p= 12.66Ω

Ques 9. For the given circuit below, calculate the equivalent resistance between the end points A and B. (3 marks)

Ans. The exp-ression for the equivalent resistance of the resistor connected in series is-

R_S = R₁ + R₂ + R₃

R_S = 2Ω + 3Ω + 4Ω

R_S = 3Ω

For Latest Updates on Upcoming Board Exams, Click Here:https://t.me/class_10_12_board_updates

Also Check:

Study Guide
NCERT Solutions for Class 12 Biology	Class 12 Chemistry Practical	Class 12 chemistry notes
Class 12 Notes	NCERT Solutions for Class 12 English	NCERT Solutions for Class 12
Class 12 physics Practical	NCERT Solutions for Class 12 Maths	NCERT Class 12 Textbook
Class 12 Physics Notes	Class 12 Biology Notes	Class 12 Mathematics Notes
NCERT Solutions for Class 12 Chemistry	NCERT Class 12 Biology Book	NCERT Class 12 Physics Book PDF
NCERT Class 12 Maths PDF	NCERT Solutions for Class 12 Physics	NCERT Class 12 English PDF
Class 11 physics notes	NCERT Solutions for Class 11 Maths	NCERT Class 11 Chemistry Book PDF
NCERT Solutions for Class 11 Chemistry	NCERT Solutions for Class 11	NCERT Class 11 Physics Book
Mendeleev's Periodic Table	Class 11 Notes	NCERT Class 11 Biology Book PDF
NCERT Solutions for Class 11 Biology	NCERT Solutions for Class 11 English	NCERT Solutions for Class 11 Physics

Equivalent Resistance Formula: Series And Parallel Circuit Example

What is Equivalent Resistance?

Current Electricity Detailed Video Explanation:

Series Arrangement of Resistance

Parallel Arrangement of Resistance

Things to Remember

Previous Year Questions

Sample Questions

CBSE CLASS XII Related Questions

1.
Four independent waves are expressed as \[ (i)\; y_1=A_1\sin\omega t, \] \[ (ii)\; y_2=A_2\sin 2\omega t, \] \[ (iii)\; y_3=A_3\cos\omega t, \] \[ (iv)\; y_4=A_4\sin\left(\omega t+\frac{\pi}{3}\right) \] The interference between two of these waves is possible in

2.
Draw a circuit diagram of a full-wave rectifier using p-n junction diodes. Explain its working and show the input-output waveforms.

3.
Photoemission of electrons occurs from a metal (\( \phi_0 = 1.96 \, \text{eV} \)) when light of frequency \( 6.4 \times 10^{14} \, \text{Hz} \) is incident on it. Calculate: Energy of a photon in the incident light, The maximum kinetic energy of the emitted electrons, and The stopping potential.

4.
Write any two features of nuclear forces.

5.
What is displacement current (\( i_d \))? Considering the case of charging of a capacitor, show that \( i_d = \varepsilon_0 \frac{d\Phi_E}{dt} \). What is the value of \( i_d \) for a conductor across which a constant voltage is applied?

6.
If both the number of protons and the neutrons are conserved in each nuclear reaction, in what way is mass converted into energy (or vice versa) in a nuclear reaction? Explain.

Similar Physics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

Equivalent Resistance Formula: Series And Parallel Circuit Example

What is Equivalent Resistance?

Current Electricity Detailed Video Explanation:

Series Arrangement of Resistance

Parallel Arrangement of Resistance

Things to Remember

Previous Year Questions

Sample Questions

CBSE CLASS XII Related Questions

1.Four independent waves are expressed as \[ (i)\; y_1=A_1\sin\omega t, \] \[ (ii)\; y_2=A_2\sin 2\omega t, \] \[ (iii)\; y_3=A_3\cos\omega t, \] \[ (iv)\; y_4=A_4\sin\left(\omega t+\frac{\pi}{3}\right) \] The interference between two of these waves is possible in

2.Draw a circuit diagram of a full-wave rectifier using p-n junction diodes. Explain its working and show the input-output waveforms.

3.Photoemission of electrons occurs from a metal (\( \phi_0 = 1.96 \, \text{eV} \)) when light of frequency \( 6.4 \times 10^{14} \, \text{Hz} \) is incident on it. Calculate: Energy of a photon in the incident light, The maximum kinetic energy of the emitted electrons, and The stopping potential.

4. Write any two features of nuclear forces.

5.What is displacement current (\( i_d \))? Considering the case of charging of a capacitor, show that \( i_d = \varepsilon_0 \frac{d\Phi_E}{dt} \). What is the value of \( i_d \) for a conductor across which a constant voltage is applied?

6. If both the number of protons and the neutrons are conserved in each nuclear reaction, in what way is mass converted into energy (or vice versa) in a nuclear reaction? Explain.

Similar Physics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Four independent waves are expressed as \[ (i)\; y_1=A_1\sin\omega t, \] \[ (ii)\; y_2=A_2\sin 2\omega t, \] \[ (iii)\; y_3=A_3\cos\omega t, \] \[ (iv)\; y_4=A_4\sin\left(\omega t+\frac{\pi}{3}\right) \] The interference between two of these waves is possible in

2.
Draw a circuit diagram of a full-wave rectifier using p-n junction diodes. Explain its working and show the input-output waveforms.

3.
Photoemission of electrons occurs from a metal (\( \phi_0 = 1.96 \, \text{eV} \)) when light of frequency \( 6.4 \times 10^{14} \, \text{Hz} \) is incident on it. Calculate: Energy of a photon in the incident light, The maximum kinetic energy of the emitted electrons, and The stopping potential.

4.
Write any two features of nuclear forces.

5.
What is displacement current (\( i_d \))? Considering the case of charging of a capacitor, show that \( i_d = \varepsilon_0 \frac{d\Phi_E}{dt} \). What is the value of \( i_d \) for a conductor across which a constant voltage is applied?

6.
If both the number of protons and the neutrons are conserved in each nuclear reaction, in what way is mass converted into energy (or vice versa) in a nuclear reaction? Explain.