A moving-coil instrument gives a full-scale deflection if 20 mA flows through it. The resistance of the coil is 2 . Calculate:

To use the instrument as an ammeter, a shunt resistor ($R_{sh}$) is connected in parallel with the meter. The total current ($I$) is $1 \text{ A}$.
The current flowing through the shunt resistor is the total current minus the current flowing through the meter:

$$I_{sh} = I - I_m$$ $$I_{sh} = 1 \text{ A} - 0.020 \text{ A}$$ $$I_{sh} = 0.980 \text{ A}$$

Since the shunt resistor is in parallel with the meter, the voltage across them is the same ($V_{sh} = V_m$).

$$I_{sh} R_{sh} = I_m R_m$$ $$R_{sh} = \frac{I_m R_m}{I_{sh}}$$

Substitute the values:

$$R_{sh} = \frac{(0.020 \text{ A})(2 \text{ } \Omega)}{0.980 \text{ A}}$$ $$R_{sh} = \frac{0.040 \text{ } \Omega}{0.980}$$ $$R_{sh} \approx 0.0408 \text{ } \Omega$$

The required shunt resistance is $\boxed{\text{}0.0408 \text{ } \Omega\text{}}$

To use the instrument as a voltmeter, a series resistor ($R_{se}$) is connected in series with the meter. The maximum voltage ($V$) to be measured is $10 \text{ V}$.
At full-scale deflection, the total resistance ($R_{total}$) of the voltmeter circuit is given by Ohm's law:

$$R_{total} = \frac{V}{I_m}$$ $$R_{total} = \frac{10 \text{ V}}{0.020 \text{ A}}$$ $$R_{total} = 500 \text{ } \Omega$$

The total resistance is the sum of the meter's resistance and the series resistance:

$$R_{total} = R_m + R_{se}$$ $$R_{se} = R_{total} - R_m$$

Substitute the values:

$$R_{se} = 500 \text{ } \Omega - 2 \text{ } \Omega$$ $$R_{se} = 498 \text{ } \Omega$$

The required series resistance is $\boxed{\text{}498 \text{ } \Omega\text{}}$

2. What material are shunt resistors made of? Why?

Shunt resistors are typically made of materials like Manganin or Constantan.

These materials are chosen for shunt resistors primarily because they have a very low temperature coefficient of resistance. This means their resistance changes very little with variations in temperature, ensuring that the ammeter's accuracy is maintained even when the instrument heats up due to current flow. They also have high resistivity and low thermal electromotive force (EMF) against copper.