Equivalent Circuits - Understanding Cells in series
- Cells connected in series form an equivalent circuit
- Total potential difference across the circuit is the sum of individual cell voltages
- Current is the same through each cell
- Useful formula: Total potential difference = n * EMF (n: number of cells in series)
Explaining EMF
- EMF stands for Electromotive Force
- EMF of a cell is the energy converted from non-electrical form to electrical form per unit charge passing through it
- EMF represents the total electrical energy supplied by the cell per unit charge
- EMF is measured in volts
Characteristics of Cells in series
- The positive terminal of one cell is connected to the negative terminal of the next cell
- The negative terminal of the first cell and the positive terminal of the last cell are connected to the external circuit
- Cells in series increase the overall potential difference
- Example: Two cells of 2V and 3V connected in series will result in a total potential difference of 5V
Internal Resistance of a Cell
- Internal resistance is the resistance offered by the electrolyte inside the cell
- It is in series with the cell’s EMF
- Internal resistance is responsible for the loss of potential difference across the cell
- Internal resistance affects the overall resistance of the circuit
Equivalent Circuit with Internal Resistance
- A cell can be represented as an EMF source in parallel with its internal resistance
- The current through the circuit is determined by the overall resistance of the circuit
- Equation: I = E / (R + r) (I: current, E: EMF, R: external resistance, r: internal resistance)
Calculating Potential Difference across External Resistance
- Using Ohm’s Law: V = IR (V: potential difference, I: current, R: resistance)
- Applying Ohm’s Law to the circuit with internal resistance: V = [E / (R + r)] * R
- Simplifying the equation: V = ER / (R + r)
Maximum Power Transfer Theorem
- Maximum power is transferred to the external resistance when it is equal to the internal resistance
- Equation for maximum power transfer: P = (E^2 * R)/(4r)
- It is important to match the load resistance with the internal resistance for maximum power transfer
Power Dissipated in Internal Resistance
- The power dissipated in the internal resistance of the cell is given by: P_r = (E^2) / (4r)
- Power dissipated in internal resistance is wasted as heat
- Efficiency of a cell can be determined by comparing power dissipated in internal resistance to power delivered to the external circuit
Experimental Verification
- Experimental setup consists of various cells in series with an ammeter and a variable resistor
- The external resistance is varied and the corresponding current and potential difference are measured
- Graphs can be plotted to observe the relationship between current, potential difference, and resistance in the circuit
Example Problem 1
- Two cells of 6V and 8V are connected in series. Calculate the total potential difference across the circuit.
- Solution: Total potential difference = 6V + 8V = 14V
Equivalent Circuits - Understanding Cells in series
- Cells connected in series form an equivalent circuit
- Total potential difference across the circuit is the sum of individual cell voltages
- Current is the same through each cell
- Useful formula: Total potential difference = n * EMF (n: number of cells in series)
Explaining EMF
- EMF stands for Electromotive Force
- EMF of a cell is the energy converted from non-electrical form to electrical form per unit charge passing through it
- EMF represents the total electrical energy supplied by the cell per unit charge
- EMF is measured in volts
Characteristics of Cells in series
- The positive terminal of one cell is connected to the negative terminal of the next cell
- The negative terminal of the first cell and the positive terminal of the last cell are connected to the external circuit
- Cells in series increase the overall potential difference
- Example: Two cells of 2V and 3V connected in series will result in a total potential difference of 5V
Internal Resistance of a Cell
- Internal resistance is the resistance offered by the electrolyte inside the cell
- It is in series with the cell’s EMF
- Internal resistance is responsible for the loss of potential difference across the cell
- Internal resistance affects the overall resistance of the circuit
Equivalent Circuit with Internal Resistance
- A cell can be represented as an EMF source in parallel with its internal resistance
- The current through the circuit is determined by the overall resistance of the circuit
- Equation: I = E / (R + r) (I: current, E: EMF, R: external resistance, r: internal resistance)
Calculating Potential Difference across External Resistance
- Using Ohm’s Law: V = IR (V: potential difference, I: current, R: resistance)
- Applying Ohm’s Law to the circuit with internal resistance: V = [E / (R + r)] * R
- Simplifying the equation: V = ER / (R + r)
Maximum Power Transfer Theorem
- Maximum power is transferred to the external resistance when it is equal to the internal resistance
- Equation for maximum power transfer: P = (E^2 * R)/(4r)
- It is important to match the load resistance with the internal resistance for maximum power transfer
Power Dissipated in Internal Resistance
- The power dissipated in the internal resistance of the cell is given by: P_r = (E^2) / (4r)
- Power dissipated in internal resistance is wasted as heat
- Efficiency of a cell can be determined by comparing power dissipated in internal resistance to power delivered to the external circuit
Experimental Verification
- Experimental setup consists of various cells in series with an ammeter and a variable resistor
- The external resistance is varied and the corresponding current and potential difference are measured
- Graphs can be plotted to observe the relationship between current, potential difference, and resistance in the circuit
Example Problem 1
- Two cells of 6V and 8V are connected in series. Calculate the total potential difference across the circuit.
- Solution: Total potential difference = 6V + 8V = 14V
Equivalent Circuits - Understanding Cells in series
- Cells connected in series form an equivalent circuit
- Total potential difference across the circuit is the sum of individual cell voltages
- Current is the same through each cell
- Useful formula: Total potential difference = n * EMF (n: number of cells in series)
Explaining EMF
- EMF stands for Electromotive Force
- EMF of a cell is the energy converted from non-electrical form to electrical form per unit charge passing through it
- EMF represents the total electrical energy supplied by the cell per unit charge
- EMF is measured in volts
Characteristics of Cells in series
- The positive terminal of one cell is connected to the negative terminal of the next cell
- The negative terminal of the first cell and the positive terminal of the last cell are connected to the external circuit
- Cells in series increase the overall potential difference
- Example: Two cells of 2V and 3V connected in series will result in a total potential difference of 5V
Internal Resistance of a Cell
- Internal resistance is the resistance offered by the electrolyte inside the cell
- It is in series with the cell’s EMF
- Internal resistance is responsible for the loss of potential difference across the cell
- Internal resistance affects the overall resistance of the circuit
Equivalent Circuit with Internal Resistance
- A cell can be represented as an EMF source in parallel with its internal resistance
- The current through the circuit is determined by the overall resistance of the circuit
- Equation: I = E / (R + r) (I: current, E: EMF, R: external resistance, r: internal resistance)
Calculating Potential Difference across External Resistance
- Using Ohm’s Law: V = IR (V: potential difference, I: current, R: resistance)
- Applying Ohm’s Law to the circuit with internal resistance: V = [E / (R + r)] * R
- Simplifying the equation: V = ER / (R + r)
Maximum Power Transfer Theorem
- Maximum power is transferred to the external resistance when it is equal to the internal resistance
- Equation for maximum power transfer: P = (E^2 * R)/(4r)
- It is important to match the load resistance with the internal resistance for maximum power transfer
Power Dissipated in Internal Resistance
- The power dissipated in the internal resistance of the cell is given by: P_r = (E^2) / (4r)
- Power dissipated in internal resistance is wasted as heat
- Efficiency of a cell can be determined by comparing power dissipated in internal resistance to power delivered to the external circuit
Experimental Verification
- Experimental setup consists of various cells in series with an ammeter and a variable resistor
- The external resistance is varied and the corresponding current and potential difference are measured
- Graphs can be plotted to observe the relationship between current, potential difference, and resistance in the circuit
Example Problem 1
- Two cells of 6V and 8V are connected in series. Calculate the total potential difference across the circuit.
- Solution: Total potential difference = 6V + 8V = 14V
Equivalent Circuits - Understanding Cells in series Cells connected in series form an equivalent circuit Total potential difference across the circuit is the sum of individual cell voltages Current is the same through each cell Useful formula: Total potential difference = n * EMF (n: number of cells in series)