Question

How to convert galvanometer to ammeter?

Answer 1

Converting a galvanometer into an ammeter involves using a shunt resistor. A galvanometer is designed to measure small currents and is typically calibrated to show the deflection of a needle in response to the current passing through it. To enable it to measure larger currents (like an ammeter), you'll need to divert most of the current away from the galvanometer itself. Here’s a detailed step-by-step guide on how to do this:

### Step 1: Understand the Galvanometer

1. **Working Principle**: A galvanometer is based on the principle that a magnetic field is produced when an electric current passes through a coil, causing a needle to deflect. The amount of deflection is proportional to the current.
2. **Full-Scale Deflection**: Identify the maximum current (I_g) the galvanometer can measure before reaching full-scale deflection. This is usually provided in the galvanometer’s specifications.

### Step 2: Determine the Maximum Current to Measure

1. **Desired Current Range**: Decide the maximum current (I) you want the ammeter to measure. For example, you might want to convert a galvanometer that measures up to 1 mA to measure up to 10 A.

### Step 3: Calculate the Shunt Resistor Value

1. **Use the Formula**: The shunt resistor (R_sh) must be calculated using the formula derived from Ohm's Law:
   \[
   R_{sh} = \frac{V_g}{I - I_g}
   \]
   where:
   - \( V_g \) is the voltage across the galvanometer when it reads maximum current (\( V_g = I_g \cdot R_g \)).
   - \( I \) is the total current you want to measure.
   - \( I_g \) is the maximum current for the galvanometer.
   - \( R_g \) is the internal resistance of the galvanometer.

2. **Example Calculation**:
   - Let’s say \( I_g = 1 \text{ mA} \) and \( R_g = 1000 \, \Omega \).
   - For a total current \( I = 10 \text{ A} \):
     \[
     V_g = I_g \cdot R_g = 0.001 \, A \cdot 1000 \, \Omega = 1 \, V
     \]
     \[
     R_{sh} = \frac{1 \, V}{10 \, A - 0.001 \, A} = \frac{1}{9.999} \approx 0.1 \, \Omega
     \]

### Step 4: Connect the Shunt Resistor

1. **Placement**: Connect the shunt resistor in parallel with the galvanometer. This allows most of the current to bypass the galvanometer while a small fraction (equal to \( I_g \)) passes through it.
2. **Wiring**: Make sure the connections are secure and that the shunt resistor can handle the power without overheating.

### Step 5: Calibration

1. **Testing**: After connecting the shunt, test the ammeter with known currents to ensure that it reads correctly. Adjust if necessary.
2. **Marking the Scale**: If the galvanometer has a dial, you may need to calibrate it to indicate the correct values for the total current being measured.

### Step 6: Safety Considerations

1. **Power Rating**: Ensure the shunt resistor has an adequate power rating to handle the maximum current without burning out. The power can be calculated as:
   \[
   P = I^2 \cdot R_{sh}
   \]
2. **Avoid Overcurrent**: Ensure that the current flowing through the galvanometer does not exceed its maximum rating to avoid damage.

### Conclusion

By carefully selecting and connecting a shunt resistor, you can successfully convert a galvanometer into an ammeter, allowing it to measure larger currents while protecting the galvanometer from excessive current. This method retains the original functionality of the galvanometer while expanding its usability in various applications.

Answer 2

To convert a galvanometer into an ammeter, you need to connect a low-resistance shunt (also known as a shunt resistor) in parallel with the galvanometer. This allows the majority of the current to bypass the sensitive galvanometer coil, protecting it from high current levels while still enabling it to measure current effectively. Here’s a detailed explanation of the process:

### 1. **Understanding the Galvanometer:**
   - **Galvanometer** is a device that detects and measures small electric currents. It has:
     - **High sensitivity**: It can measure very small currents (usually in microamperes or milliamperes).
     - **High internal resistance**: It is designed to respond to small currents, so it is not capable of handling large currents without damage.
     - **Full-scale deflection current (Ig)**: This is the maximum current that the galvanometer can handle before the needle reaches full-scale deflection (usually a very small value like 10-50 milliamperes).
     
   Since a galvanometer is designed to measure small currents, it cannot directly measure large currents. To convert it into an **ammeter** that measures higher currents, a shunt resistor must be added.

### 2. **Ammeter Basics:**
   - An **ammeter** is a device used to measure electric current flowing through a circuit.
   - It is connected in series with the circuit, so it needs to have very low resistance so that it doesn't significantly affect the total resistance of the circuit.
   
   The ammeter needs to be able to measure large currents without damaging the galvanometer.

### 3. **Shunt Resistor (Rₛ):**
   The purpose of the shunt resistor is to "bypass" most of the current around the galvanometer. Since the galvanometer is delicate and can only handle a small current, the shunt resistor allows a larger portion of the current to flow through it while only a small fraction of the current passes through the galvanometer.

   The shunt resistor is connected **in parallel** with the galvanometer. Here’s why:
   - According to **Kirchhoff's Current Law**, the total current entering a junction (or parallel connection) equals the sum of the currents through each branch.
   - The larger current will mostly pass through the shunt resistor because it has a much lower resistance than the galvanometer.

### 4. **Formula for Shunt Resistance:**
   Let’s say:
   - **I** is the total current that you want to measure with the ammeter.
   - **Ig** is the maximum current that the galvanometer can handle (full-scale deflection current).
   - **Rg** is the internal resistance of the galvanometer.
   - **Rs** is the resistance of the shunt resistor.

   The relationship between these variables is given by:

   \[
   R_s = \frac{I_g \cdot R_g}{I - I_g}
   \]

   This formula ensures that the shunt resistor has the correct value to bypass the excess current, allowing only the maximum safe current (**Ig**) to pass through the galvanometer.

   - **I - Ig** is the current that will pass through the shunt resistor.
   - The galvanometer and the shunt resistor share the same voltage (since they are in parallel).

### 5. **Procedure to Convert a Galvanometer into an Ammeter:**

   **Step 1: Measure the resistance of the galvanometer (Rg).**
   - The internal resistance of the galvanometer is usually provided by the manufacturer or can be measured using an ohmmeter.

   **Step 2: Determine the maximum current (Ig) the galvanometer can handle.**
   - This value is also usually specified for the galvanometer.

   **Step 3: Decide the range of current (I) the new ammeter should measure.**
   - For example, if you want to measure currents up to 10 A, you set this as the maximum current (**I**).

   **Step 4: Calculate the shunt resistance (Rs).**
   - Using the formula mentioned above, calculate the resistance of the shunt resistor needed.

   **Step 5: Connect the shunt resistor in parallel with the galvanometer.**
   - Once the shunt resistor is selected, connect it in parallel to the galvanometer. The combination will now function as an ammeter.

### 6. **Example Calculation:**
   Suppose you have:
   - A galvanometer with internal resistance **Rg = 100 ohms**.
   - Maximum full-scale deflection current **Ig = 10 mA (0.01 A)**.
   - You want to convert this galvanometer into an ammeter that can measure up to **I = 10 A**.

   Using the formula for the shunt resistance:

   \[
   R_s = \frac{0.01 \times 100}{10 - 0.01}
   \]

   \[
   R_s = \frac{1}{9.99}
   \]

   \[
   R_s ≈ 0.1001 \, \Omega
   \]

   So, the shunt resistor should have a value of approximately **0.1 ohms** to allow the galvanometer to measure up to 10 A.

### 7. **Precautions:**
   - Make sure the shunt resistor is able to handle the power dissipation (P = I²R).
   - The connection of the shunt should be firm and secure to ensure accurate current measurement.
   - Ensure that the galvanometer is properly calibrated after conversion to give accurate current readings.

### 8. **Summary of Steps:**
   1. Find the internal resistance of the galvanometer (**Rg**) and its full-scale deflection current (**Ig**).
   2. Decide the current range (**I**) for the ammeter.
   3. Calculate the required shunt resistance (**Rs**).
   4. Connect the shunt resistor in parallel with the galvanometer.
   5. Your galvanometer is now converted into an ammeter capable of measuring higher currents.

By adding the appropriate shunt resistor, the galvanometer can safely measure large currents without damage, and you have successfully created an ammeter!