A galvanometer with a coil of resistance 120 ohm shows full scale deflection for a current of 2.5 mA. How will you convert the galvanometer into an amm- eter of range 0 to 7.5 A? Determine the net resistance of the ammeter. When an ammeter is put in a circuit, does it read slightly less or more than the actual current in the original circuit? Justify your answer ?

To convert a galvanometer into an ammeter that can measure a higher current range, such as 0 to 7.5 A, you need to use a shunt resistor. This shunt resistor will allow most of the current to bypass the galvanometer, protecting it from damage while still providing an accurate measurement of the total current flowing in the circuit. Let's break down the steps to determine the necessary shunt resistor and the total resistance of the ammeter.

Understanding the Galvanometer Specifications

The galvanometer's full-scale deflection occurs at a current of 2.5 mA, with a coil resistance of 120 ohms. This means that when 2.5 mA flows through the galvanometer, it shows the maximum reading. To convert this into an ammeter that can measure up to 7.5 A, we will need to calculate the appropriate shunt resistor.

Calculating the Shunt Resistor

First, we need to determine the voltage across the galvanometer when it shows full-scale deflection:

• Voltage (Vg) = Current (Ig) × Resistance (Rg)
• Vg = 2.5 mA × 120 ohms = 0.0025 A × 120 ohms = 0.3 V

Next, we need to find the total current (I) that will flow through the ammeter when it is in use, which is 7.5 A. The current flowing through the galvanometer (Ig) will still be 2.5 mA (0.0025 A), while the current passing through the shunt resistor (Is) can be calculated as follows:

• Is = I - Ig
• Is = 7.5 A - 0.0025 A = 7.4975 A

The voltage across the shunt resistor (Vs) must equal the voltage across the galvanometer (Vg) to ensure proper functioning:

• Vs = Vg = 0.3 V

Now, we can use Ohm's law to find the resistance of the shunt resistor (Rs):

• Rs = Vs / Is
• Rs = 0.3 V / 7.4975 A ≈ 0.0400 ohms

Net Resistance of the Ammeter

The net resistance of the ammeter is the combination of the galvanometer's resistance and the shunt resistor. Since the shunt resistor is in parallel with the galvanometer, we can use the formula for parallel resistances:

• 1/R_total = 1/Rg + 1/Rs

Substituting the values we know:

• 1/R_total = 1/120 + 1/0.0400
• 1/R_total = 0.00833 + 25
• 1/R_total = 25.00833
• R_total ≈ 0.0399 ohms

Impact on Current Readings

When you connect an ammeter in a circuit, it is designed to have very low resistance to minimize its impact on the overall current. However, because it still has some resistance, it does affect the current slightly. In practice, the reading on the ammeter will often be slightly less than the actual current in the circuit due to the voltage drop across its internal resistance.

This means that while the ammeter measures the current flowing through it, the actual current in the circuit might be marginally higher than what the ammeter displays. The difference is usually negligible, especially if the ammeter is designed with very low resistance.

In summary, to convert the galvanometer to an ammeter for a range of 0 to 7.5 A, you need a shunt resistor of approximately 0.0400 ohms, resulting in a net resistance of around 0.0399 ohms for the ammeter. Keep in mind that the ammeter's reading will be slightly less than the true current due to its own resistance, affecting the circuit's total current flow. This design ensures that you can measure high currents safely without damaging the sensitive galvanometer component.