EXPERIMENT: DETERMINATION OF CHARGE SENSITIVITY OF BALLISTIC GALVANOMETER
1. AIM
To determine the charge sensitivity of a ballistic galvanometer using a known capacitor.
2. APPARATUS USED
- Ballistic Galvanometer
- Battery (6V)
- Standard Capacitor (of known capacitance)
- High Resistance Box
- Resistance Box
- One-way Key
- Two-way Key
- Rheostat
- Ammeter
- Voltmeter
- Connecting Wires
- Lamp and Scale Arrangement
3. DIAGRAM
Figure 1: Circuit diagram for determining the charge sensitivity of a ballistic galvanometer
4. THEORY
A ballistic galvanometer is designed to measure the quantity of charge that passes through it in a short period of time. When a transient current passes through a ballistic galvanometer, the coil experiences a mechanical impulse, causing it to deflect. The first throw or swing of the galvanometer is proportional to the total charge that passes through it.
The charge sensitivity of a ballistic galvanometer is defined as the charge required to produce a deflection of one scale division on the galvanometer. It is denoted by 'k' and is measured in coulombs per scale division (C/div).
In this experiment, we discharge a capacitor of known capacitance 'C' through the ballistic galvanometer. The capacitor is first charged to a potential difference 'V' and then discharged through the galvanometer. The total charge 'Q' passing through the galvanometer is:
$Q = CV$
where:
- Q = Total charge in coulombs (C)
- C = Capacitance of the capacitor in farads (F)
- V = Potential difference across the capacitor in volts (V)
If θ is the first deflection or throw of the galvanometer (in scale divisions), then the charge sensitivity 'k' is given by:
$k = \frac{Q}{\theta} = \frac{CV}{\theta}$
This relationship assumes that the damping is small and can be neglected. For greater accuracy, we can take multiple readings with different values of voltage and calculate the average value of the charge sensitivity.
5. FORMULA
The charge sensitivity of the ballistic galvanometer is given by:
$k = \frac{CV}{\theta}$
where:
k = Charge sensitivity in coulomb/division (C/div)
C = Capacitance of the capacitor in farads (F)
V = Potential difference across the capacitor in volts (V)
θ = First throw or deflection of the galvanometer in scale divisions
6. PROCEDURE
- Set up the apparatus as shown in the circuit diagram.
- Keep the two-way key 'K' in position 1 initially (open position).
- Set the rheostat to a suitable value to control the current from the battery.
- Adjust the lamp and scale arrangement to get a clear reflection from the galvanometer mirror.
- Note the zero reading of the galvanometer on the scale.
- Press the two-way key to position 2 to charge the capacitor to potential V, as measured by the voltmeter.
- Quickly move the key to position 3 to discharge the capacitor through the galvanometer.
- Observe and record the first throw or deflection (θ) of the galvanometer on the scale.
- Repeat steps 6-8 for the same voltage several times and take the average value of deflection.
- Change the voltage and repeat steps 6-9 for different values of V.
- Calculate the charge sensitivity using the formula k = CV/θ for each observation.
- Calculate the mean value of k.
7. OBSERVATION TABLE
| S.No. | Capacitance C (μF) | Potential Difference V (volts) | First Deflection θ (scale divisions) | Charge Sensitivity k = CV/θ (μC/div) |
|---|---|---|---|---|
| 1 | ||||
| 2 | ||||
| 3 | ||||
| 4 | ||||
| 5 | ||||
| Mean value of charge sensitivity (k) | ||||
8. CALCULATIONS
For each observation:
$k = \frac{CV}{\theta}$
Example calculation for the first observation:
Given:
- Capacitance (C) = ___ μF = ___ × 10-6 F
- Potential difference (V) = ___ volts
- Deflection (θ) = ___ scale divisions
$k = \frac{C \times V}{\theta} = \frac{___ \times 10^{-6} \times ___}{___} = ___ \times 10^{-6}$ coulomb/division
$k = ___ \times 10^{-6}$ C/div = ___ μC/div
Mean value of charge sensitivity:
$k_{mean} = \frac{k_1 + k_2 + k_3 + k_4 + k_5}{5} = ___ μC/div$
9. RESULT
The charge sensitivity of the given ballistic galvanometer is ___ × 10-6 coulomb/division or ___ μC/div.
10. PRECAUTIONS
- The ballistic galvanometer should be placed on a stable, vibration-free surface.
- The galvanometer should be properly leveled before starting the experiment.
- The capacitor should be completely discharged before each observation.
- The capacitor should be of good quality with minimal leakage.
- The discharge of the capacitor through the galvanometer should be quick to ensure that the entire charge passes through it in a short time.
- The lamp and scale arrangement should be properly adjusted to get clear readings.
- The experiment should be performed in a room free from air currents to avoid unwanted vibrations of the galvanometer coil.
- All connections should be tight and clean to avoid contact resistance.
- The capacitor should be charged to the same potential difference for multiple readings at the same voltage.
- Earth's magnetic field should be properly taken into account (the galvanometer should be aligned with the magnetic meridian).
11. VIVA VOICE QUESTIONS
Q1. What is a ballistic galvanometer?
A ballistic galvanometer is a sensitive electrical instrument designed to measure the quantity of electrical charge passing through it in a very short time interval. It operates on the principle that the first deflection of the galvanometer is proportional to the total charge passing through it.
Q2. What is the charge sensitivity of a ballistic galvanometer?
The charge sensitivity of a ballistic galvanometer is defined as the amount of charge required to produce a deflection of one scale division. It is typically expressed in coulombs per division (C/div) or microcoulombs per division (μC/div).
Q3. How does a ballistic galvanometer differ from an ordinary galvanometer?
An ordinary galvanometer measures steady currents and gives a deflection proportional to the current, while a ballistic galvanometer measures the total charge passing through it in a very short time and gives a deflection proportional to the charge. Ballistic galvanometers have heavy coils with high moment of inertia to ensure the coil doesn't start moving significantly until the entire charge has passed through.
Q4. Why is a capacitor used in this experiment?
A capacitor is used because it can store a known quantity of charge (Q = CV), which can then be discharged through the galvanometer. By knowing the capacitance (C) and the voltage (V) to which it was charged, we can calculate the total charge passing through the galvanometer.
Q5. How does damping affect the reading of a ballistic galvanometer?
Damping reduces the amplitude of oscillations of the galvanometer coil. In a ballistic galvanometer, excessive damping would reduce the first throw and lead to erroneous results. However, some amount of damping is necessary to bring the coil to rest quickly after the measurement. In the calculation of charge sensitivity, we assume the damping is small enough to be neglected.
Q6. What are the sources of error in this experiment?
Sources of error include: capacitor leakage, contact resistance in connections, magnetic disturbances affecting the galvanometer, improper alignment of the galvanometer, parallax errors in reading the scale, fluctuations in the battery voltage, and inaccuracies in the known value of the capacitor.
Q7. Can we use this method to measure an unknown capacitance?
Yes, once the charge sensitivity of the ballistic galvanometer is determined, we can use it to measure an unknown capacitance. The unknown capacitor is charged to a known potential and then discharged through the galvanometer. From the deflection, we can calculate the charge and hence the capacitance using the formula C = Q/V.
Q8. Why is it important to discharge the capacitor completely before each observation?
If the capacitor is not completely discharged before charging it again, it may lead to residual charge remaining in the capacitor. This would result in an incorrect voltage reading and consequently an erroneous calculation of the charge sensitivity.
Q9. What would happen if a very large capacitor is used in this experiment?
If a very large capacitor is used, it would store a large amount of charge at the same voltage. When discharged through the galvanometer, it might cause the deflection to go beyond the scale's range, making accurate measurements difficult. Additionally, the discharge time might become significant, violating the assumption of instantaneous discharge required for the ballistic principle.
Q10. How does temperature affect the charge sensitivity of a ballistic galvanometer?
Temperature can affect the resistance of the galvanometer coil, the strength of the magnetic field, and the elasticity of the suspension. An increase in temperature increases the resistance of the coil, reducing the current for the same potential difference. It also reduces the magnetic field strength. Both these factors can change the charge sensitivity of the galvanometer.