A moving-coil instrument with a resistance of 5 and a full-scale deflection current of 20 mA is to be converted into an ammeter to measure a total current of 3 A. Calculate the required shunt resistan

The resistance of the moving-coil instrument is $R_m = 5 \, \Omega$.
The full-scale deflection current of the instrument is $I_m = 20 \, \text{mA} = 0.020 \, \text{A}$.
The total current to be measured is $I = 3 \, \text{A}$.

When a shunt resistor is connected in parallel with the instrument, the total current $I$ splits between the instrument current $I_m$ and the shunt current $I_{sh}$.

Therefore, the current through the shunt resistor is:

Since the shunt resistor is in parallel with the instrument, the voltage across both components is the same.
The voltage across the instrument is:

The voltage across the shunt resistor is equal to the voltage across the instrument, $V_{sh} = V_m = 0.1 \, \text{V}$.
Using Ohm's Law for the shunt resistor:

The shunt resistance required is $\text{0.0336 } \Omega$.