To convert a galvanometer into a voltmeter, we need to add a resistor in series with the galvanometer. This resistor, known as a shunt resistor, allows us to extend the range of the galvanometer to measure higher voltages without damaging the instrument. Let's break down the problem step by step to find the required resistance for a range of 0V to 5V.
Understanding the Galvanometer Specifications
The galvanometer has the following specifications:
- Resistance of the galvanometer (Rg) = 90 ohms
- Full-scale deflection voltage (Vg) = 225 mV = 0.225 V
Calculating the Required Series Resistance
To convert the galvanometer into a voltmeter that can measure up to 5V, we need to determine the total resistance (R_total) required for this voltage. The total voltage across the galvanometer and the series resistor (Rs) must equal the maximum voltage we want to measure:
Using Ohm's Law, we can express this relationship as:
V = I * R
Where:
- V is the total voltage (5V)
- I is the current through the galvanometer at full-scale deflection
- R is the total resistance (Rg + Rs)
Finding the Current at Full Scale
First, we need to find the current (I) that corresponds to the full-scale deflection of the galvanometer:
Using Ohm's Law:
I = Vg / Rg = 0.225 V / 90 ohms = 0.0025 A (or 2.5 mA)
Setting Up the Voltage Equation
Now, we can set up the equation for the total voltage:
5V = I * (Rg + Rs)
Substituting the value of I:
5V = 0.0025 A * (90 ohms + Rs)
Solving for Rs
Rearranging the equation to solve for Rs:
5V / 0.0025 A = 90 ohms + Rs
2000 = 90 + Rs
Rs = 2000 - 90 = 1910 ohms
Final Configuration
To convert the galvanometer into a voltmeter with a range of 0V to 5V, you should connect a resistor of 1910 ohms in series with the galvanometer. This configuration allows the galvanometer to measure the higher voltage while ensuring that the current through it remains within safe limits for full-scale deflection.
In summary, the required resistance to convert the galvanometer into a voltmeter for a range of 0V to 5V is 1910 ohms, and it should be connected in series with the galvanometer. This setup will allow you to accurately measure voltages up to 5V without damaging the galvanometer.
