Animated Solution for Physics - Current Electricity: For the post office box arrangement to determine the value of unknown resistance, the unknown resistance should be connected between

Imagine you are in a physics laboratory, tasked with finding the exact value of an unknown resistor. The instrument placed before you is a Post Office Box. It might look like a simple wooden box with brass blocks and plugs, but it is essentially a highly compact and practical version of the classic Wheatstone bridge.

The Wheatstone bridge operates on a beautiful principle of symmetry. It consists of four resistive arms forming a closed loop. When the bridge is balanced, no current flows through the galvanometer, and the ratio of the resistances in the ratio arms perfectly equals the ratio of the known resistance to the unknown resistance.

Let's look closely at the schematic provided in the question. The top row features terminals $B$, $C$, and $D$. The resistances plugged in between $B$ and $C$, and between $C$ and $D$, serve as the ratio arms of our bridge. These arms typically provide a multiplier ratio like $10:1$ or $100:1$.

The rest of the brass blocks, winding from terminal $D$ through the middle row and down to the bottom row ending at terminal $A$, form a massive series of resistors. This entire zig-zag path constitutes the known resistance arm, often referred to as the rheostat arm.

Now, according to the standard configuration for this specific arrangement, the arms $BC$, $CD$, and $BA$ are considered the known resistances within the internal circuitry of the box. To complete the closed loop of the Wheatstone bridge and make the circuit functional, we need to connect our unknown resistance to form the fourth and final arm.

Since the internal known resistances occupy the paths between $B$, $C$, $D$, and $A$, the only logical places left to connect the external unknown resistance are the terminals $A$ and $D$. By connecting it here, we complete the bridge, allowing us to adjust the known resistance until the galvanometer shows a null deflection.

Therefore, we can confidently conclude that the unknown resistance must be connected between terminals $A$ and $D$. This makes option (c) the correct choice. It's a classic question that tests not just your theoretical knowledge, but your familiarity with the physical layout of laboratory instruments!