SP Unit 2.3
Practicals
DC Circuits
SP Unit 2.3PracticalsDC CircuitsLearners should be able to demonstrate and apply their knowledge and understanding of: |
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| 1. | Determination of the Internal Resistance of a cell |
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Determination of the Internal Resistance of a Cell
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⇒ Theoretical Background
- A cell (battery) is not an ideal voltage source; it has an internal resistance r that causes the terminal voltage to drop under load. The cell’s electromotive force (emf), E, and its internal resistance are related to the terminal voltage V when a load is connected by the equation:
- [math]E = V + Ir[/math]
- Where:
- – I is the current flowing through the circuit,
- – V is the voltage measured across the load.
- Rearranging, the internal resistance can be calculated as:
- [math]r = \frac{E – V}{I}[/math]
- Alternatively, if a known load resistor [math]R_L[/math] is used, the current I can be calculated from Ohm’s law:
- [math]I = \frac{V}{R_L}[/math]
- Then, combining the equations, we get:
- [math]r = R_L \left( \frac{E – V}{V} \right)[/math]
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⇒ Apparatus and Materials
- A battery or cell to be tested
- A digital voltmeter
- A set of known resistors or a variable resistor (rheostat)
- Connecting wires and clips
- An ammeter (optional, if separate current measurement is desired)
- A switch for circuit control (optional)
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⇒ Experimental Procedure
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Step 1: Measure Open-Circuit Voltage
- 1. Setup:
- – Connect the voltmeter directly across the cell terminals with no load attached.
- 2. Measurement:
- – Record the open-circuit voltage, E. This is the emf of the cell.
- Figure 1 To determine the internal resistance
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Step 2: Apply a Known Load
- 1. Connect Load Resistor:
- – Attach a known resistor across the cell terminals. The resistor should be chosen so that a measurable current flows without causing excessive voltage drop or overheating.
- 2. Measure Loaded Voltage:
- – With the load connected, measure the terminal voltage V across [math]R_L[/math] using the voltmeter.
- 3. Calculate Current:
- – Determine the current I flowing through the circuit using Ohm’s law:
- [math]I = \frac{V}{R_L}[/math]
- 4. Determine Internal Resistance:
- – Use the formula:
- [math]r = \frac{E – V}{I}[/math]
- Or equivalently
- [math]r = R_L \left( \frac{E – V}{V} \right)[/math]
- – Calculate the internal resistance from your measured values.
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Step 3: Repeat for Accuracy
- For increased reliability, repeat the measurements with different values of [math]R_L[/math].
- Plotting V against I can also be done; the slope of the line fitting the data (from the relationship [math]E = Ir + V[/math]) can give the internal resistance r.
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Step 4: Data Analysis and Error Considerations
- ⇒ Data Analysis:
- – For each load, record E (open-circuit), V (loaded voltage), and I.
- – Calculate r for each trial and then average the values.
- ⇒ Error Considerations:
- – Voltmeter Accuracy: Ensure that the voltmeter is properly calibrated.
- – Connection Resistance: Poor connections can add extra resistance.
- – Load Selection: Choose [math]R_L[/math] so that the current is within a sensitive and safe range.
- – Battery Condition: The cell should be fresh; repeated high current draws may cause the battery to heat and alter its internal resistance.
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Step 5: Conclusion
- This experiment uses the relationship between open-circuit voltage and loaded voltage to determine the internal resistance of a cell. By measuring the voltage with and without a known load and calculating the current, we can use the formula:
- [math]r = \frac{E – V}{I}[/math]
- Or
- [math]r = R_L \left( \frac{E – V}{V} \right)[/math]
- to accurately determine the cell’s internal resistance. Repeating the experiment with different loads and averaging results helps reduce errors and improve accuracy.