Consider a galvanometer shunted with 5 $$\Omega$$ resistance and 2% of current passes through it. What is the resistance of the given galvanometer?

We have a galvanometer of unknown resistance $$G$$ connected in parallel with a shunt resistance $$S = 5\;\Omega$$. Both elements share the same potential difference because they are in parallel. Let the total current entering the parallel combination be $$I$$. According to the statement, only 2 % of this total current flows through the galvanometer.

Hence the current through the galvanometer is $$I_g = 0.02\,I$$ and the current through the shunt is $$I_s = I - I_g = I - 0.02\,I = 0.98\,I$$.

For two resistors in parallel, the potential drops are equal, so we write the condition

$$I_g\,G = I_s\,S.$$

Substituting the expressions for $$I_g$$ and $$I_s$$ we get

$$0.02\,I \, G = 0.98\,I \, S.$$

We can cancel the common factor $$I$$ from both sides, giving

$$0.02\,G = 0.98\,S.$$

Now we isolate $$G$$ by dividing both sides by $$0.02$$:

$$G = \frac{0.98}{0.02}\,S.$$

Next we calculate the numerical ratio:

$$\frac{0.98}{0.02} = \frac{98}{2} = 49.$$

So we obtain

$$G = 49\,S.$$

Substituting the given value of the shunt resistance $$S = 5\;\Omega$$, we have

$$G = 49 \times 5\;\Omega = 245\;\Omega.$$

Hence, the correct answer is Option A.