How do you convert a galvanometer into an ammeter and calculate the shunt resistance needed for a 10A range?

Question

ScanSolve AI Tutor · Accepted Answer

To convert a galvanometer into an ammeter, a low resistance resistor, called a shunt resistor, is connected in parallel with the galvanometer.

Identify the given values.
Galvanometer full-scale deflection current, $I_g = 10 \, \text{mA} = 10 \times 10^{-3} \, \text{A} = 0.01 \, \text{A}$
Galvanometer coil resistance, $R_g = 30 \, \Omega$
Desired ammeter range (total current), $I = 10 \, \text{A}$
Determine the current through the shunt resistor.
When the galvanometer and shunt resistor are in parallel, the total current $I$ splits between them.
The current through the shunt resistor, $I_{sh}$ , is given by:
$I_{sh} = I - I_g$ $I_{sh} = 10 \, \text{A} - 0.01 \, \text{A}$ $I_{sh} = 9.99 \, \text{A}$
Calculate the voltage across the galvanometer.
The voltage across the galvanometer at full-scale deflection is:
$V_g = I_g R_g$ $V_g = (0.01 \, \text{A})(30 \, \Omega)$ $V_g = 0.3 \, \text{V}$
Calculate the shunt resistance.
Since the galvanometer and the shunt resistor are in parallel, the voltage across them is the same ( $V_g = V_{sh}$ ).
$V_{sh} = I_{sh} R_{sh}$
Therefore,
$R_{sh} = \frac{V_{sh}}{I_{sh}} = \frac{V_g}{I_{sh}}$ $R_{sh} = \frac{0.3 \, \text{V}}{9.99 \, \text{A}}$ $R_{sh} \approx 0.03003 \, \Omega$
Choose the correct option.
The calculated shunt resistance is approximately $0.03 \, \Omega$ . Since it must be a shunt resistor (connected in parallel), the correct option is B.

The final answer is $\boxed{\text{B. 0.03\Omega shunt resistor}}$

Answer