CAPACITANCE

Sp Unit 4.1

Practicals

Capacitance

Sp Unit 4.1 Practicals Capacitance Learners should be able to demonstrate and apply their knowledge and understanding of:
1.	Investigation of the charging and discharging of a capacitor to determine the time constant
2.	Investigation of the energy stored in a capacitor

Sp Unit 4.1

Practicals

Learners should be able to demonstrate and apply their knowledge and understanding of:

Investigation of the charging and discharging of a capacitor to determine the time constant

Investigation of the energy stored in a capacitor

1. Investigation of the charging and discharging of a capacitor to determine the time constant
⇒ Objective:
To study the charging and discharging process of a capacitor in a RC circuit and determine its time constant (τ=RC).
⇒ Apparatus Required:
– A capacitor (e.g., 1000 µF)
– A resistor (e.g., 10 kΩ)
– A DC power supply (e.g., 9V battery)
– A switch
– A voltmeter (or oscilloscope)
– A stopwatch
– Connecting wires
⇒ Theory:
When a capacitor charges through a resistor, the voltage across it follows:
[math]V = V_0 \left(1 – e^{-\frac{t}{RC}}\right)[/math]
When it discharges, the voltage follows:
[math]V = V_0 e^{-\frac{t}{RC}}[/math]
Where:
– [math]V_o[/math] = initial voltage
– R = resistance (Ω)
– C = capacitance (F)
– t = time (s)
– [math]τ = RC[/math] is the time constant, the time taken for the voltage to decrease to 37% of its initial value.
⇒ Procedure:
Charging Phase:
1. Set up the circuit with the capacitor, resistor, power supply, and switch in series.
2. Close the switch to allow current to flow and start the charging process.
3. Record voltage readings across the capacitor every 5 seconds until it reaches close to the supply voltage.
4. Plot a graph of V vs. t. The curve should show an exponential increase.
Figure 1 Charging phase of capacitor
Discharging Phase:
1. Open the switch and remove the power supply.
2. Record the voltage every 5 seconds as the capacitor discharges.
3. Plot a graph of V vs. t. The curve should show an exponential decay.
4. Determine the time constant (τ) by finding the time when voltage reaches 37% of [math]V_o[/math]
Figure 2 Discharging phase of capacitor
⇒ Results & Analysis:
– The charging curve follows an exponential rise.
– The discharging curve follows an exponential decay.
– The time constant (τ) is determined from the decay curve.
⇒ Precautions & Errors:
– Use low-leakage capacitors for accuracy.
– Ensure the resistor value is large enough to slow the process.
– Use a digital voltmeter for precise readings.
⇒ Conclusion:
This experiment demonstrates that a capacitor charges and discharges exponentially. The time constant (τ) is the key parameter governing the process.
2. Investigation Of the Energy Stored In A Capacitor
⇒ Objective:
To measure the energy stored in a capacitor and verify the formula:
[math]E = \frac{1}{2} C V^2[/math]
Where:
– E = stored energy (J)
– C = capacitance (F)
– V = voltage (V)
⇒ Apparatus Required:
– A capacitor (e.g., 1000 µF)
– A resistor (e.g., 1 kΩ)
– A DC power supply (9V battery)
– A switch
– A voltmeter
– A Joule meter or a method to measure power dissipation
Figure 3 Energy stored in a capacitor
⇒ Procedure:
Charging Phase:
1. Connect the circuit with the capacitor, resistor, power supply, and switch.
2. Close the switch to start charging the capacitor.
3. Measure the voltage across the capacitor at regular intervals.
4. Use the formula [math]E = \frac{1}{2} C V^2[/math] to calculate the stored energy.
Discharging Phase (Energy Transfer to a Load):
1. Disconnect the power supply and connect the capacitor to a known resistor.
2. Measure the current and voltage as the capacitor discharges.
3. Calculate the power dissipated using [math]P = VI[/math] and integrate over time to find the energy released.
4. Compare this with the theoretical energy stored ([math] \frac{1}{2} C V^2[/math] ).
⇒ Results & Analysis:
– The measured energy closely matches the theoretical energy.
– Small differences may be due to resistance losses and capacitor inefficiencies.
⇒ Precautions & Errors:
– Ensure good connections to reduce resistance losses.
– Use a high-precision voltmeter for accurate readings.
– Minimize leakage current from the capacitor.
⇒ Conclusion:
This experiment confirms that the energy stored in a capacitor is given by [math]E = \frac{1}{2} C V^2[/math]. The energy transfer can be observed by discharging the capacitor through a resistor.