Animated Solution for Physics - Current Electricity: Which of the following statements is false?

The Wheatstone bridge is one of the most beautiful and symmetrical circuits in classical electromagnetism. It consists of four resistances—$P$, $Q$, $R$, and $S$—arranged in a diamond shape. A galvanometer is connected across one diagonal (say, between nodes B and D), and a voltage source is connected across the other diagonal (between nodes A and C).

When the bridge is balanced, the potential at node B is exactly equal to the potential at node D ($V_B=V_D$). Because there is no potential difference across the galvanometer, no current flows through it ($I_g=0$). The mathematical condition for this perfect balance is given by the ratio:

Swapping Components

Now, let's tackle the core of the question. What happens if we physically exchange the positions of the battery and the galvanometer?

Imagine disconnecting the battery from nodes A and C, and reconnecting it across nodes B and D. Simultaneously, we take the galvanometer and connect it across nodes A and C.

If we analyze this new configuration from the perspective of the new battery terminals (B and D), the bridge arms have effectively rotated. For the galvanometer (now across A and C) to show zero deflection, the new balance condition requires the ratio of the new adjacent arms to be equal:

At first glance, $\frac{P}{R}=\frac{Q}{S}$ looks like a different requirement than our original condition. But let's look closer at the original equation:

If we simply cross-multiply the terms $Q$ and $R$, the equation transforms into:

It is the exact same mathematical relationship! This proves that if a Wheatstone bridge is balanced in its standard configuration, it remains perfectly balanced even if you swap the battery and the galvanometer. The null point is absolutely not disturbed. Therefore, statement (a) is false.

To ensure complete conceptual clarity, let's quickly review why the other statements are true:

(b) A rheostat can be used as a potential divider: A rheostat is a variable resistor with a sliding contact. By connecting across the fixed ends and tapping the sliding contact, it acts exactly like a potentiometer, dividing the input voltage. (c) Kirchhoff's second law represents energy conservation: Kirchhoff's Voltage Law (KVL) states that the sum of potential differences around any closed loop is zero. Since electric potential is potential energy per unit charge, this is a direct restatement of the law of conservation of energy. (d) Wheatstone bridge is most sensitive when all four resistances are of the same order:* Sensitivity refers to the galvanometer's deflection for a small fractional change in an unknown resistance. Mathematical analysis shows that this deflection is maximized when $P\approx Q\approx R\approx S$.