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 / 0.3Ω
1 / R_total = 10Ω + 5Ω + 3.333Ω
1 / R_total = 18.333Ω
- Therefore, the total resistance is:
R_total = 1 / 18.333Ω ≈ 0.0545Ω
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.