Stepwise Derivation and Formula for Conversion of Galvanometer to Ammeter and Voltmeter
The conversion of galvanometer to ammeter and voltmeter is a key topic in JEE Physics, focusing on adapting a sensitive moving coil galvanometer for measuring larger currents (as an ammeter) or potential differences (as a voltmeter). Understanding this concept helps students master circuit measurements and confidently solve practical problems involving meter conversions and resistor arrangements.
A galvanometer on its own detects very small currents, not full circuit values. With the right shunt or series resistor, it can accurately work as an ammeter or voltmeter in current electricity experiments. This is fundamental for topics like resistance, Ohm’s law, and Kirchhoff’s laws.
In this page, all key formulas, stepwise circuit methods, and crucial exam strategies around the conversion of galvanometer to ammeter and voltmeter are provided, with a special focus on derivations and errors commonly seen in JEE Main questions.
Conversion of Galvanometer to Ammeter: Method & Formula
To convert a galvanometer into an ammeter, connect a shunt resistor (very low resistance, S) in parallel with the galvanometer (resistance G). This allows most of the current to bypass the sensitive coil, protecting the instrument and extending its range.
The key principle is based on parallel circuits, where the shunt carries extra current such that the galvanometer never exceeds its maximum safe value (Ig). This concept aligns with parallel circuits rules you study for JEE Physics.
| Quantity | Symbol | Typical Value | SI Unit |
|---|---|---|---|
| Galvanometer resistance | G | 10–100 | Ω |
| Shunt resistance | S | Tiny (see below) | Ω |
| Full-scale current (ammeter) | I | Up to 1 A or more | A |
| Galvanometer max current | Ig | 0.01–0.05 | A |
- Shunt is always in parallel with galvanometer for ammeter conversion.
- Ammeters need very low total resistance to avoid altering circuit current.
- The moving coil galvanometer is chosen for its high sensitivity and uniform scale.
- An ideal ammeter has near zero resistance (practically, as low as possible).
Ammeter conversion formula:
To calculate the value of shunt resistance needed:
| Shunt Resistance (S) | S = (Ig × G) / (I - Ig) |
|---|
Where:
- I = maximum current to be measured (ammeter range)
- Ig = full-scale deflection current of galvanometer
- G = resistance of galvanometer
- Decide the range for new ammeter (I).
- Obtain galvanometer specs (Ig and G).
- Compute S using the above formula.
- Connect S in parallel to galvanometer.
This setup is often examined alongside measurement error or current division questions. Further practice can be found at experimental skills mock test.
Conversion of Galvanometer to Voltmeter: Circuit, Formula & Steps
For the conversion of galvanometer to voltmeter, a high resistance (R) is connected in series with the galvanometer. This increases the range, so the device can safely measure larger potential differences without exceeding the coil's current rating.
A voltmeter must not draw significant current or load the circuit, so the added series resistance ensures its own current stays minimal. This directly uses Ohm’s law and ties to the difference between series and parallel circuits in current electricity.
- Series resistance is always added for voltmeter conversion.
- Ideal voltmeter has infinite resistance (practically, very high resistance).
Voltmeter conversion formula:
To achieve a desired voltage range, calculate required series resistance:
| Total Series Resistance (R) | R = (V / Ig) - G |
|---|
Where:
- V = maximum voltage to be measured (voltmeter range)
- Ig = galvanometer full-scale deflection current
- G = resistance of galvanometer
- Set desired range (V) for the voltmeter.
- Know galvanometer values (Ig and G).
- Find extra resistance (R) needed using the formula.
- Connect R in series with galvanometer.
Many JEE-type numericals require you to reverse engineer this process or compare the voltmeter and ammeter readings in multi-meter setups.
Key Principles: Why Shunt and Series Resistances?
Both conversions use the basic principle that the current through the galvanometer must never exceed its safe limit (Ig).
- In ammeter conversion, the shunt is a bypass so most current avoids the delicate coil.
- In voltmeter conversion, the high series resistance limits current for high voltage drops.
- This ensures accurate measurements and protects the instrument.
- Both methods use Ohm’s law and rules of series and parallel arrangements.
Typical JEE Numericals: Conversion of Galvanometer to Ammeter and Voltmeter
Apply the conversion of galvanometer to ammeter and voltmeter formulas precisely, showing units throughout. Below are sample solved numericals.
-
A galvanometer has G = 30 Ω, Ig = 20 mA. What shunt (S) turns it into a 2 A ammeter?
S = (Ig × G)/(I – Ig) = (0.02 × 30)/(2 – 0.02) = 0.6/1.98 ≈ 0.303 Ω
-
Find series resistance R to convert above galvanometer (same specs) into a voltmeter of 10 V range.
R = (V/Ig) – G = (10/0.02) – 30 = 500 – 30 = 470 Ω
-
If a required S is connected improperly in series, what happens?
The ammeter reads abnormally low, as full current cannot pass. This is a wrong connection.
-
Calculate the resistance of an ideal ammeter and voltmeter in this context.
Zero for ammeter, infinite for voltmeter as per JEE exam conventions.
For more practice, refer to the Vedantu JEE Physics practice papers and current electricity numericals.
Common Pitfalls and Tips: Galvanometer Conversion
- Forget to distinguish between parallel (ammeter) and series (voltmeter) conversion.
- Omit or misapply Ohm’s law during calculations.
- Use wrong value for Ig (should be in amperes).
- Neglect to subtract G from total R in voltmeter.
- Ignore the resistance of wires or connection errors.
| Aspect | Galvanometer → Ammeter | Galvanometer → Voltmeter |
|---|---|---|
| Resistor arrangement | Shunt (parallel) | Series (high resistance) |
| Overall device resistance | Very low | Very high |
| Ideal value (theory) | 0 Ω | ∞ Ω |
| Main formula | S = (IgG)/(I–Ig) | R = (V/Ig) – G |
Experiments on the conversion of galvanometer to ammeter and voltmeter strengthen practical skills. Detailed steps and equipment lists can also be found in Vedantu experimental skills revision notes.
- Record G and Ig via standard calibration circuit.
- Compute S or R as per above formulas for your range (I or V).
- Assemble the circuit. Use proper connections and tight contact points.
- Verify readings with known currents/voltages as per lab protocols.
Mastery of the conversion of galvanometer to ammeter and voltmeter boosts confidence in current electricity, measurement, and lines of JEE Main physics questions. Sharpen your calculations and practical understanding by practicing more numericals and reviewing circuit diagram rules.
For further revision, visit Vedantu’s physics formulas for JEE Main and moving coil galvanometer concept.
FAQs on How to Convert a Galvanometer into an Ammeter or Voltmeter
1. What is the formula to convert galvanometer to ammeter?
To convert a galvanometer into an ammeter, a low-value shunt resistance is connected in parallel.
The formula for the shunt (S) is:
S = (Itotal × G) / (Ig - Itotal)
Where:
- G: Galvanometer resistance
- Ig: Maximum current for full-scale deflection of galvanometer
- Itotal: Maximum current to be measured by the ammeter
This method enables accurate measurement of higher currents using a galvanometer as an ammeter.
2. How do you convert a galvanometer into a voltmeter?
To convert a galvanometer into a voltmeter, a high-value resistance is added in series with the galvanometer coil.
The formula for series resistance (R) is:
R = (V / Ig) - G
Where:
- V: Desired potential difference to measure
- Ig: Current for full-scale deflection
- G: Resistance of the galvanometer
This increases the instrument's range so it can measure higher voltages safely and accurately.
3. Why is a shunt used while converting a galvanometer to an ammeter?
A shunt resistance is used to bypass most of the current around the galvanometer.
The key roles of the shunt are:
- To protect the sensitive coil from large currents
- To allow only a small, safe current through the galvanometer
- To enable the converted ammeter to measure large currents
This makes the galvanometer suitable for ammeter application by extending its range.
4. What is the principle of conversion of galvanometer into voltmeter?
The principle is to increase the galvanometer's resistance so it measures potential difference without drawing significant current.
This is done by:
- Connecting a high resistance in series (series resistance)
- Ensuring the galvanometer operates within its safe current range
- Spanning a higher voltage for the same current
Thus, the galvanometer becomes sensitive to voltage, functioning as a voltmeter.
5. What is the difference between shunt and series resistance in galvanometer conversion?
Shunt and series resistances are used for different conversions of the galvanometer:
- Shunt (parallel resistor) is used to convert a galvanometer into an ammeter (measures current).
- Series resistance (high resistor in series) is used to convert a galvanometer into a voltmeter (measures voltage).
This difference is crucial for practical and examination purposes.
6. Can the same galvanometer be used as both ammeter and voltmeter?
Yes, the same moving coil galvanometer can be converted into both an ammeter and a voltmeter by using appropriate resistors.
- To make an ammeter, connect a low-value shunt in parallel.
- To make a voltmeter, connect a high-value resistance in series.
But, the modifications are not simultaneously reversible in a single setup — you'd need to rewire the circuit for each conversion.
7. What are common mistakes to avoid during the conversion of galvanometer to ammeter or voltmeter?
Some frequent mistakes students make include:
- Mixing up shunt and series resistance purpose
- Using incorrect formulae for calculations
- Not accounting for the galvanometer's maximum allowable current (Ig)
- Connecting resistors incorrectly in series/parallel
- Ignoring the polarity and terminal connections
Always double-check the circuit and calculations to ensure accuracy in practicals and exams.
8. What happens if the wrong value of shunt is used during conversion?
Using an incorrect shunt resistance can lead to instrument malfunction or damage.
Potential consequences:
- The galvanometer may receive excess current and burn out.
- The ammeter readings become inaccurate.
- Inaccurate lower range can affect experiment outcomes.
Always use the calculated shunt for safe and accurate results.
9. Does converting a galvanometer affect its sensitivity?
Yes, conversions affect the sensitivity of the instrument.
- When converted to an ammeter (using shunt), sensitivity to small currents decreases.
- When converted to a voltmeter (using high series resistance), the sensitivity to small voltage changes increases.
This explains why different resistor values are crucial for optimal performance.
10. Why do we prefer moving coil galvanometers for conversion into ammeter and voltmeter?
Moving coil galvanometers are preferred due to their high accuracy and sensitivity.
Advantages include:
- Linear scale response for both current and voltage
- Less affected by external magnetic fields
- Low power consumption
- Quick, reliable readings in practicals and exams
This makes them ideal for conversion into both ammeter and voltmeter in laboratory and theoretical applications.
