Understanding the Concept:
To convert a delicate galvanometer of coil resistance $G$ into an ammeter capable of measuring large currents up to range $I$, a small shunt resistor ($S$) must be connected in parallel across it. The value of $S$ is calculated using the current division relationship:
\[
I_g \cdot G = (I - I_g) \cdot S \implies S = \frac{I_g \cdot G}{I - I_g}
\]
where $I_g$ represents the full-scale deflection current capacity of the galvanometer.
Step 1: Calculate full-scale deflection current limit ($I_g$).
We are given:
Total scale divisions $= 30\text{ div}$
Deflection factor $= 1\text{ mA/div} = 1 \times 10^{-3}\text{ A/div}$
Coil internal resistance, $G = 50\text{ }\Omega$
Evaluating total safe full-scale operational current boundary lines:
\[
I_g = 30\text{ div} \times 1\text{ mA/div} = 30\text{ mA} = 0.03\text{ A}
\]
Step 2: Substitute parameters into the parallel shunt expression.
Target extended line current limit, $I = 10\text{ A}$:
\[
S = \frac{0.03 \times 50}{10 - 0.03} = \frac{1.5}{9.97} \approx 0.15045\text{ }\Omega \approx 0.15\text{ }\Omega
\]