KVL states that the sum of potential differences around any closed loop is zero, which follows from the conservation of energy: the total energy gained and lost by a charge going around a closed loop must balance out. (Kirchhoff's Current Law, by contrast, is based on conservation of charge.)

If [latex]I_g = 0.1I[/latex] flows through the galvanometer, [latex]I_s = 0.9I[/latex] flows through the shunt. Since [latex]I_g G = I_s S[/latex]: [latex](90) = (0.9I)(S) \Rightarrow S = \dfrac{9}{0.9} = 10\Omega[/latex].

KVL states that the sum of potential differences around any closed loop is zero, which follows from conservation of energy: the total energy gained and lost by a charge traversing a closed loop must balance to zero.

A low-resistance shunt in parallel diverts most of the current around the galvanometer, allowing the ammeter to measure large currents without damaging the sensitive galvanometer coil; connecting resistance in series (with a high resistance) is instead how a galvanometer is converted into a voltmeter.

Potential gradient [latex]K = \dfrac{I\rho}{A} = \dfrac{(0.1)(10^{-7})}{10^{-6}} = \dfrac{10^{-8}}{10^{-6}} = 10^{-2},V/m[/latex].