A galvanometer with a coil resistance of 9Ω is used with a shunt resistor to make a non-digital ammeter that has an equivalent resistance of 0.40Ω. The current in the shunt resistor is 3 mA when the galvanometer reads full scale. Find the full-scale current of the galvanometer.
Question
A galvanometer with a coil resistance of 9Ω is used with a shunt resistor to make a non-digital ammeter that has an equivalent resistance of 0.40Ω. The current in the shunt resistor is 3 mA when the galvanometer reads full scale. Find the full-scale current of the galvanometer.
Solution
To solve this problem, we need to use the concept of parallel resistances and Ohm's law.
Step 1: Find the resistance of the shunt resistor (Rs)
The total resistance (Rt) of the ammeter is the parallel resistance of the galvanometer (Rg) and the shunt resistor (Rs). The formula for parallel resistances is:
1/Rt = 1/Rg + 1/Rs
We know Rt = 0.40Ω and Rg = 9Ω. Substituting these values into the formula, we get:
1/0.40 = 1/9 + 1/Rs
Solving for Rs, we get Rs = 0.44Ω.
Step 2: Find the full-scale current of the galvanometer (Ig)
The current in the shunt resistor (Is) is 3 mA. According to Ohm's law (V = IR), the voltage across the shunt resistor (Vs) is:
Vs = Is * Rs = 0.003 * 0.44 = 0.00132V
Since the galvanometer and the shunt resistor are in parallel, the voltage across the galvanometer (Vg) is the same as Vs. Therefore, we can use Ohm's law to find the full-scale current of the galvanometer:
Ig = Vg / Rg = 0.00132 / 9 = 0.000147A or 147 μA.
So, the full-scale current of the galvanometer is 147 μA.
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