Series And Parallel Combinations Of Cells
- Current and Electricity - An introduction
Learning Objectives
- Understand the concept of series and parallel combinations of cells
- Learn how current flows in series and parallel circuits
- Understand the calculated results of voltage and current in different configurations
- Apply Ohm’s Law to solve circuit problems involving series and parallel combinations of cells
Introduction
- In electronic circuits, multiple cells or batteries are often connected together to provide the required voltage and current.
- There are two common methods of connecting cells in circuits: series and parallel combinations.
- In this lecture, we will explore the behavior of cells connected in series and parallel, and analyze their effect on voltage and current.
Series Combination of Cells
- When cells are connected in series:
- The positive terminal of one cell is connected to the negative terminal of the next cell.
- The total voltage of the combination is the sum of individual cell voltages.
- The total emf (electromotive force) of the series combination is given by:
Emf_total = Emf_1 + Emf_2 + Emf_3 + ...
Series Combination of Cells (contd.)
- The current flowing through each cell in a series combination is the same.
- The total internal resistance of the series combination is the sum of individual internal resistances.
- The total internal resistance (R_total) is given by:
R_total = R_1 + R_2 + R_3 + ... - The total resistance of the series combination is also equal to the sum of individual resistances of the cells.
Example - Series Combination of Cells
- Consider three cells with emf values of 1.5V, 2V, and 3V connected in series.
- The internal resistances of the cells are 0.1Ω, 0.2Ω, and 0.3Ω respectively.
- What is the total emf and internal resistance of the series combination?
- Solution:
- Emf_total = 1.5V + 2V + 3V = 6.5V
- R_total = 0.1Ω + 0.2Ω + 0.3Ω = 0.6Ω
Parallel Combination of Cells
- When cells are connected in parallel:
- The positive terminals of all cells are connected together and similarly, the negative terminals are connected together.
- The total emf (Emf_total) of the parallel combination is the same as the emf of each individual cell.
- The total internal resistance (R_total) of the parallel combination is given by:
1 / R_total = 1 / R_1 + 1 / R_2 + 1 / R_3 + ...
Parallel Combination of Cells (contd.)
- The current divides among the cells in a parallel combination.
- The sum of currents through each cell is equal to the total current.
- The resistance of the total parallel combination (R_total) is less than the smallest resistance of any individual cell.
Example - Parallel Combination of Cells
- Consider three cells with emf values of 1.5V, 2V, and 3V connected in parallel.
- The internal resistances of the cells are 0.1Ω, 0.2Ω, and 0.3Ω respectively.
- Calculate the total emf and internal resistance of the parallel combination.
- Solution:
- Emf_total = Emf_1 = Emf_2 = Emf_3 = 1.5V
- 1 / R_total = 1 / R_1 + 1 / R_2 + 1 / R_3
- 1 / R_total = 1 / 0.1Ω + 1 / 0.2Ω + 1 / 0.3Ω
- R_total = 0.1667Ω
Voltage and Current in Series and Parallel Combinations
- In series combination, the current is the same through all cells, while the voltage divides among the cells.
- In parallel combination, the voltage is the same across all cells, while the current divides among the cells.
- Ohm’s Law can be applied to calculate the current, voltage, and resistance in the series and parallel combinations.
- The total resistance in series combination is the sum of individual resistances, while in parallel combination it is less than the smallest resistance.
Series And Parallel Combinations Of Cells
- Current and Electricity - An introduction
Learning Objectives
- Understand the concept of series and parallel combinations of cells
- Learn how current flows in series and parallel circuits
- Understand the calculated results of voltage and current in different configurations
- Apply Ohm’s Law to solve circuit problems involving series and parallel combinations of cells
Introduction
- In electronic circuits, multiple cells or batteries are often connected together to provide the required voltage and current.
- There are two common methods of connecting cells in circuits: series and parallel combinations.
- In this lecture, we will explore the behavior of cells connected in series and parallel, and analyze their effect on voltage and current.
Series Combination of Cells
- When cells are connected in series:
- The positive terminal of one cell is connected to the negative terminal of the next cell.
- The total voltage of the combination is the sum of individual cell voltages.
- The total emf (electromotive force) of the series combination is given by:
Emf_total = Emf_1 + Emf_2 + Emf_3 + ...
Series Combination of Cells (contd.)
- The current flowing through each cell in a series combination is the same.
- The total internal resistance of the series combination is the sum of individual internal resistances.
- The total internal resistance (R_total) is given by:
R_total = R_1 + R_2 + R_3 + ...
- The total resistance of the series combination is also equal to the sum of individual resistances of the cells.
Example - Series Combination of Cells
- Consider three cells with emf values of 1.5V, 2V, and 3V connected in series.
- The internal resistances of the cells are 0.1Ω, 0.2Ω, and 0.3Ω respectively.
- What is the total emf and internal resistance of the series combination?
- Solution:
- Emf_total = 1.5V + 2V + 3V = 6.5V
- R_total = 0.1Ω + 0.2Ω + 0.3Ω = 0.6Ω
Parallel Combination of Cells
- When cells are connected in parallel:
- The positive terminals of all cells are connected together and similarly, the negative terminals are connected together.
- The total emf (Emf_total) of the parallel combination is the same as the emf of each individual cell.
- The total internal resistance (R_total) of the parallel combination is given by:
1 / R_total = 1 / R_1 + 1 / R_2 + 1 / R_3 + ...
Parallel Combination of Cells (contd.)
- The current divides among the cells in a parallel combination.
- The sum of currents through each cell is equal to the total current.
- The resistance of the total parallel combination (R_total) is less than the smallest resistance of any individual cell.
Example - Parallel Combination of Cells
- Consider three cells with emf values of 1.5V, 2V, and 3V connected in parallel.
- The internal resistances of the cells are 0.1Ω, 0.2Ω, and 0.3Ω respectively.
- Calculate the total emf and internal resistance of the parallel combination.
- Solution:
- Emf_total = Emf_1 = Emf_2 = Emf_3 = 1.5V
- 1 / R_total = 1 / R_1 + 1 / R_2 + 1 / R_3
- 1 / R_total = 1 / 0.1Ω + 1 / 0.2Ω + 1 / 0.3Ω
- R_total = 0.1667Ω
Voltage and Current in Series and Parallel Combinations
- In series combination, the current is the same through all cells, while the voltage divides among the cells.
- In parallel combination, the voltage is the same across all cells, while the current divides among the cells.
- Ohm’s Law can be applied to calculate the current, voltage, and resistance in the series and parallel combinations.
- The total resistance in series combination is the sum of individual resistances, while in parallel combination it is less than the smallest resistance.
Example - Series Combination of Cells
- Consider three cells with emf values of 1.5V, 2V, and 3V connected in series.
- If the current flowing through each cell is 0.5A, what is the total current in the series combination?
- Solution:
- The current flowing through each cell is the same, so the total current is also 0.5A.
Example - Parallel Combination of Cells
- Consider three cells with emf values of 1.5V, 2V, and 3V connected in parallel.
- If the current flowing through each cell is 1A, what is the total current in the parallel combination?
- Solution:
- The total current is the sum of currents flowing through each cell, which is 1A + 1A + 1A = 3A.
Example - Series Combination of Cells
- Consider three cells with emf values of 1.5V, 2V, and 3V connected in series.
- If the internal resistances of the cells are 0.1Ω, 0.2Ω, and 0.3Ω respectively, what is the total resistance of the series combination?
- Solution:
- The total resistance is the sum of individual resistances, which is 0.1Ω + 0.2Ω + 0.3Ω = 0.6Ω.
Example - Parallel Combination of Cells
- Consider three cells with emf values of 1.5V, 2V, and 3V connected in parallel.
- If the internal resistances of the cells are 0.1Ω, 0.2Ω, and 0.3Ω respectively, what is the total resistance of the parallel combination?
- Solution:
- The total resistance is given by the formula:
1 / R_total = 1 / R_1 + 1 / R_2 + 1 / R_3 - Substituting the values, we get:
1 / R_total = 1 / 0.1Ω + 1 / 0.2Ω + 1 / 0.3Ω1 / R_total = 10Ω + 5Ω + 3.333Ω1 / R_total = 18.333Ω - Therefore, the total resistance is:
R_total = 1 / 18.333Ω ≈ 0.0545Ω
- The total resistance is given by the formula:
Summary
- Cells can be connected in series or parallel combinations to provide the required voltage and current in electronic circuits.
- In series combination, the voltage adds up and the current remains the same.
- In parallel combination, the voltage remains the same and the current adds up.
- The total internal resistance of series combination is the sum of individual internal resistances, while in parallel combination it is less than the smallest resistance.
- Ohm’s Law can be applied to calculate the current, voltage, and resistance in series and parallel combinations.
- The total resistance in series combination is the sum of individual resistances, while in parallel combination it is less than the smallest resistance.
Series And Parallel Combinations Of Cells Current and Electricity - An introduction