(A) Working principle: A current-carrying coil in a magnetic field experiences a torque $\tau = nIAB$. This deflects the coil until balanced by restoring torque $\tau = k\theta$. At equilibrium:
$$nIAB = k\theta \Rightarrow I = \frac{k}{nAB}\theta$$
For linear scale: use a radial magnetic field (cylindrical pole pieces + soft iron core) so $B$ is always parallel to the plane of coil, making $\sin\theta = 1$ always.

(B) Shunt resistance for ammeter conversion:
$$S = \frac{I_g \cdot G}{I - I_g} = \frac{0.05 \times 49.5}{5 - 0.05} = \frac{2.475}{4.95} = 0.5\ \Omega$$

(C) For ammeter: shunt $S$ is connected in parallel with the galvanometer.