What is a shunt? Explain its function in a circuit,obtain the formula for the shunt,and explain its uses.

(N/A) Definition: $A$ shunt is a low-value resistor connected in parallel with a galvanometer to protect it and to increase its current-measuring range.
Function in Circuit:
$(i)$ Since the resistance of the shunt $(r_s)$ is much smaller than the galvanometer resistance $(R_G)$,most of the current passes through the shunt,protecting the galvanometer from damage due to high current.
$(ii)$ The equivalent resistance of the parallel combination is $R_{eq} = \frac{R_G r_s}{R_G + r_s}$. Since $R_G \gg r_s$,$R_{eq} \approx r_s$. This low resistance ensures that the original current in the circuit remains effectively unchanged.
Derivation of Formula:
Let $R_G$ be the resistance of the galvanometer and $I_G$ be the current flowing through it. Let $r_s$ be the shunt resistance and $(I - I_G)$ be the current flowing through it,where $I$ is the total current.
Since the galvanometer and shunt are in parallel,the potential difference across them is equal:
$V_G = V_s$
$I_G R_G = (I - I_G) r_s$
$r_s = \frac{I_G R_G}{I - I_G}$
Uses:
$(i)$ It protects the galvanometer from damage by high currents.
$(ii)$ It is used to convert a galvanometer into an ammeter.
$(iii)$ By choosing an appropriate value of $r_s$,the range of the ammeter can be increased.