Converting a Galvanometer into an Ammeter and Voltmeter
1. AIM
To convert a given galvanometer (of known resistance and figure of merit) into:
- An ammeter of desired range
- A voltmeter of desired range
And to verify their accuracy against standard instruments.
2. APPARATUS USED
- Galvanometer of known resistance (G) and figure of merit (k)
- Resistance box (0-10,000 Ω)
- Standard ammeter (0-1A)
- Standard voltmeter (0-15V)
- Rheostat (0-100 Ω)
- Battery/Power supply (6V or 12V)
- Connecting wires
- One-way key
- Two-way key
- Multimeter (for verification)
- Screw gauge (for measuring wire diameter if making shunts)
- Vernier calipers
- Manganin wire (for making shunts)
3. DIAGRAM
Circuit Diagram for Ammeter Conversion and Verification:
Circuit Diagram for Voltmeter Conversion and Verification:
Where:
- G: Galvanometer
- K: Key
- R: High resistance in series (for voltmeter)
- Shunt: Low resistance in parallel (for ammeter)
4. THEORY
Basic Principle:
A galvanometer is a sensitive instrument that detects small currents by the deflection of its pointer. However, it has limitations:
- It can only measure small currents (typically in microamperes or milliamperes)
- It has a high internal resistance
- It shows full-scale deflection at a very small current value
To convert a galvanometer into practical measuring instruments:
For Ammeter Conversion:
An ammeter needs to measure larger currents while maintaining low resistance in the circuit. This is achieved by connecting a small resistance (shunt) in parallel with the galvanometer. The shunt diverts most of the current around the galvanometer, allowing only a small fraction to pass through it.
For Voltmeter Conversion:
A voltmeter needs to measure potential difference while drawing minimal current from the circuit. This is achieved by connecting a high resistance in series with the galvanometer. This combination draws very little current while still allowing the galvanometer to show proportional deflection.
Mathematical Foundation:
For a galvanometer:
- Let G = Resistance of galvanometer
- Let Ig = Current required for full-scale deflection (figure of merit)
Ammeter Conversion:
To convert the galvanometer to measure current up to I amperes:
- We need a shunt resistance S such that when current I flows in the circuit, only Ig flows through the galvanometer
- By current division principle in parallel circuits:
- Current through shunt = I - Ig
- Voltage across both paths is equal: Ig × G = (I - Ig) × S
- Therefore: S = \frac{G \times I_g}{I - I_g}
Voltmeter Conversion:
To convert the galvanometer to measure voltage up to V volts:
- We need a series resistance R such that when voltage V is applied, current Ig flows through the galvanometer
- By Ohm's Law: V = I_g \times (G + R)
- Therefore: R = \frac{V}{I_g} - G
5. FORMULA
For Ammeter Conversion:
- Shunt resistance required:
S = \frac{G \times I_g}{I - I_g}Where:
- S = Shunt resistance (in ohms)
- G = Galvanometer resistance (in ohms)
- Ig = Current for full-scale deflection (in amperes)
- I = Desired range of ammeter (in amperes)
- Current through galvanometer:
I_g = I \times \frac{S}{S + G}
For Voltmeter Conversion:
- Series resistance required:
R = \frac{V}{I_g} - GWhere:
- R = Series resistance (in ohms)
- V = Desired range of voltmeter (in volts)
- Ig = Current for full-scale deflection (in amperes)
- G = Galvanometer resistance (in ohms)
- Voltage measured:
V = I_g \times (G + R)
6. PROCEDURE
A. Determination of Galvanometer Constants (if not given):
- To find galvanometer resistance (G):
- Connect the galvanometer to a Wheatstone bridge or measure directly using a multimeter in resistance mode.
- Record the value as G ohms.
- To find figure of merit (k or Ig):
- Connect the galvanometer in series with a high resistance box and a battery.
- Adjust the resistance until galvanometer shows full-scale deflection.
- Measure the current using a standard microammeter.
- The current value is the figure of merit (Ig).
B. Ammeter Conversion:
- Calculate the required shunt resistance (S) using the formula: S = \frac{G \times I_g}{I - I_g}
- Select or prepare a shunt resistance of value S ohms.
- Connect the shunt in parallel with the galvanometer.
- Setup the circuit as shown in the diagram for ammeter verification.
- Close the key and adjust the rheostat to obtain different readings.
- For each setting, record both the standard ammeter reading and the converted galvanometer (ammeter) reading.
- Verify if the readings are within acceptable limits of error.
C. Voltmeter Conversion:
- Calculate the required series resistance (R) using the formula: R = \frac{V}{I_g} - G
- Select or prepare a resistance of value R ohms.
- Connect this resistance in series with the galvanometer.
- Setup the circuit as shown in the diagram for voltmeter verification.
- Close the key and adjust the rheostat to obtain different voltage readings.
- For each setting, record both the standard voltmeter reading and the converted galvanometer (voltmeter) reading.
- Verify if the readings are within acceptable limits of error.
7. OBSERVATION TABLES
Table 1: Galvanometer Specifications
| Parameter | Value | Unit |
|---|---|---|
| Galvanometer Resistance (G) | Ω | |
| Figure of Merit (Ig) | A | |
| Full Scale Deflection | Divisions |
Table 2: Ammeter Conversion and Verification
| Observation No. | Standard Ammeter Reading (A) | Converted Ammeter Reading (A) | Error (A) | % Error |
|---|---|---|---|---|
| 1 | ||||
| 2 | ||||
| 3 | ||||
| 4 | ||||
| 5 |
Table 3: Voltmeter Conversion and Verification
| Observation No. | Standard Voltmeter Reading (V) | Converted Voltmeter Reading (V) | Error (V) | % Error |
|---|---|---|---|---|
| 1 | ||||
| 2 | ||||
| 3 | ||||
| 4 | ||||
| 5 |
8. CALCULATIONS
For Ammeter:
- Desired range of ammeter = I = _____ A
- Galvanometer resistance (G) = _____ Ω
- Current for full-scale deflection (Ig) = _____ A
- Required shunt resistance (S) = \frac{G \times I_g}{I - I_g}
= \frac{_____ \times _____}{_____ - _____}
= _____ Ω - Calculation of error:
- Error = (Reading of converted ammeter) - (Reading of standard ammeter)
- % Error = \frac{\text{Error}}{\text{Reading of standard ammeter}} \times 100
For Voltmeter:
- Desired range of voltmeter = V = _____ V
- Galvanometer resistance (G) = _____ Ω
- Current for full-scale deflection (Ig) = _____ A
- Required series resistance (R) = \frac{V}{I_g} - G
= \frac{_____}{_____} - _____
= _____ Ω - Calculation of error:
- Error = (Reading of converted voltmeter) - (Reading of standard voltmeter)
- % Error = \frac{\text{Error}}{\text{Reading of standard voltmeter}} \times 100
9. RESULT
1. The given galvanometer having resistance G = _____ Ω and figure of merit Ig = _____ A has been successfully converted into:
a) An ammeter of range _____ A by connecting a shunt resistance of _____ Ω in parallel with the galvanometer.
- The maximum percentage error in ammeter readings was found to be _____%.
b) A voltmeter of range _____ V by connecting a series resistance of _____ Ω in series with the galvanometer.
- The maximum percentage error in voltmeter readings was found to be _____%.
2. The calibration of both instruments has been verified against standard measuring devices, and the errors are within acceptable limits.
10. PRECAUTIONS
- The galvanometer should be handled carefully to prevent damage to its delicate mechanism.
- All connections should be clean, tight, and properly insulated.
- The key should be pressed only when taking observations to avoid prolonged current flow through the galvanometer.
- Start with the highest resistance in the circuit to prevent damage from excess current.
- The galvanometer should be kept away from magnetic fields and vibrations.
- The shunt resistance should be made of material having low temperature coefficient of resistance (like manganin or constantan).
- The resistance box terminals should be clean to ensure proper contact.
- When measuring current, the ammeter should always be connected in series with the circuit element.
- When measuring voltage, the voltmeter should always be connected in parallel with the circuit element.
- Verify zero error of the galvanometer before starting measurements.
- Always increase the current/voltage gradually using the rheostat.
- Avoid parallax error while taking readings from the galvanometer scale.
11. SOURCES OF ERROR
Instrumental Errors:
- Calibration errors in the standard ammeter and voltmeter
- Zero error in the galvanometer
- Resistance tolerance in the shunt or series resistors
- Internal resistance variations due to temperature changes
Observational Errors:
- Parallax error while reading the position of the pointer
- Error in reading the scales of the instruments
- Human reaction time error in simultaneous readings
Environmental Errors:
- Fluctuations in temperature affecting resistance values
- External magnetic fields affecting galvanometer readings
- Vibrations causing oscillations in the galvanometer needle
Theoretical Errors:
- Assuming the galvanometer has a linear scale
- Neglecting contact resistances in connections
- Approximations in the calculation of shunt and series resistances
12. VIVA VOCE QUESTIONS
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Q: What is the basic principle of a moving coil galvanometer?
A: A moving coil galvanometer works on the principle of electromagnetic induction. When current flows through a coil placed in a magnetic field, a torque acts on the coil causing it to rotate. The deflection is proportional to the current flowing through the coil.
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Q: What is meant by the "figure of merit" of a galvanometer?
A: The figure of merit of a galvanometer is the current required to produce a full-scale deflection. It is also known as the current sensitivity of the galvanometer and is usually expressed in amperes per division or microamperes per division.
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Q: Why is a shunt connected in parallel with the galvanometer when converting it to an ammeter?
A: A shunt is connected in parallel with the galvanometer to divert most of the current around the galvanometer. This allows the ammeter to measure currents much larger than the galvanometer's full-scale deflection current while protecting the galvanometer from damage.
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Q: Why is a high resistance connected in series with the galvanometer when converting it to a voltmeter?
A: A high resistance is connected in series to limit the current flowing through the galvanometer when measuring voltage. This ensures that the galvanometer draws minimal current from the circuit being measured, providing more accurate voltage readings.
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Q: What are the characteristics of an ideal ammeter and voltmeter?
A: An ideal ammeter has zero resistance and measures current without affecting the circuit. An ideal voltmeter has infinite resistance and measures voltage without drawing any current from the circuit.
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Q: Why are manganin or constantan wires preferred for making shunts?
A: Manganin and constantan have very low temperature coefficients of resistance, meaning their resistance remains nearly constant with temperature changes. This ensures accurate ammeter readings across varying operating temperatures.
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Q: How does the internal resistance of an ammeter affect the circuit being measured?
A: The internal resistance of an ammeter causes a voltage drop when inserted in a circuit, potentially reducing the current in the circuit. A good ammeter should have very low resistance to minimize this effect.
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Q: Can we use the same galvanometer simultaneously as both an ammeter and a voltmeter?
A: No, because the conversion requires different circuit configurations. An ammeter needs a parallel shunt, while a voltmeter needs a series resistance. These are mutually exclusive setups.
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Q: What happens if you connect an ammeter in parallel with a circuit element?
A: If an ammeter is connected in parallel, its low resistance creates a short circuit path, potentially damaging both the ammeter and the circuit due to excessive current flow.
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Q: What happens if you connect a voltmeter in series with a circuit element?
A: If a voltmeter is connected in series, its high resistance severely restricts current flow in the circuit, giving incorrect readings of both voltage and affecting the circuit operation.