Which of the following statements is false?

We begin by examining each of the four statements one by one and verifying whether it is in accordance with the well-known principles of electric circuits.

First consider Option A. Kirchhoff’s second law, also called the loop law, states that in any closed conducting loop the algebraic sum of all the electromotive forces and the potential drops is zero. Mathematically we write

$$\sum E + \sum IR = 0,$$

where $$E$$ denotes the electromotive forces in the loop and $$IR$$ represents the potential drops across resistive elements. This equation is merely an application of the law of conservation of energy, because the total energy gained by the charges from the sources equals the total energy lost across the resistances in one complete traversal of the loop. Hence Option A is a true statement.

Now look at Option B. The sensitivity of a Wheatstone bridge is defined as the deflection shown by the galvanometer per unit fractional change in one of the resistances. By theory, the sensitivity turns out to be the highest when the four resistances in the bridge are of the same order of magnitude, that is, when

$$R_1 \approx R_2 \approx R_3 \approx R_4.$$

This is because equal arms give the largest change in galvanometer current for a given small fractional change in resistance, making the bridge highly responsive. Therefore Option B is also true.

Next examine Option C. In a Wheatstone bridge the balance condition is

$$\frac{R_1}{R_2} = \frac{R_3}{R_4}.$$

If this ratio is satisfied, the potential difference between the two mid-points (to which the galvanometer is connected) is zero, so no current flows through the galvanometer and the bridge is said to be balanced (null condition). Now suppose the cell and the galvanometer are interchanged. The resistive network remains exactly the same, and the points that were at equal potential earlier are still at equal potential because the above ratio remains unaltered. Hence the null point is not disturbed; the bridge stays balanced. The statement in Option C says that the null point is disturbed, which contradicts the actual behavior. Consequently, Option C is false.

Finally consider Option D. A rheostat is simply a variable resistor. By tapping a fraction of the total resistance, one can obtain an adjustable potential difference across a portion of the resistor while the rest of the resistor drops the remaining voltage. This arrangement is popularly known as a potential divider. Because a rheostat performs exactly this function, Option D is indeed correct.

Summarising our findings: Options A, B and D are true, whereas Option C is not. Hence, the statement that is false is the one given in Option C, which corresponds to choice number 3 in the list.

Hence, the correct answer is Option C.