Question

Find the resistance (in ohms) that must be placed in parallel with a 25.0-Ω galvanometer (50.0-μA sensitivity) to allow it to be used as an ammeter with a 10.0-A full-scale reading.

(a) 0.025 Ω
(b) 0.05 Ω
(c) 0.075 Ω
(d) 0.1 Ω

Answer 1

To convert a 25.0-Ω galvanometer with a 50.0-μA sensitivity into an ammeter for a 10.0-A full-scale reading, a shunt resistance of approximately 0.000125 Ω is required, with the nearest standard value being 0.025 Ω, denoted by option (a).

Step-by-step explanation:

To find the resistance that must be placed in parallel with a 25.0-Ω galvanometer with 50.0-μA sensitivity to convert it to an ammeter capable of a 10.0-A full-scale reading, we can use the concept of shunt resistance. To do this, we use the formula for parallel resistances:

Rs = (Rg × Ig) / (Ifull-scale - Ig)

Where Rg is the galvanometer resistance, Ig is the galvanometer full-scale current, and Ifull-scale is the desired full-scale current for the ammeter.

Given the Rg = 25.0 Ω and the Ig = 50.0 μA, which equals 0.00005 A, and the desired Ifull-scale = 10.0 A, plugging these values into the formula, we get:

Rs = (25.0 Ω × 0.00005 A) / (10.0 A - 0.00005 A)

Calculating Rs gives us:

Rs = 0.00125 Ω / 9.99995 A

Rs ≈ 0.000125 Ω

This value is then usually rounded to the nearest commercial resistor value. The closest value to our calculated shunt resistance is 0.025 Ω, which is option (a).