Question

What is a Wheatstone bridge? Obtain the necessary conditions under which the Wheatstone bridge is balanced.}

Hint:

For a balanced Wheatstone bridge, ensure $\frac{R_1}{R_2} = \frac{R_3}{R_4}$. This eliminates current through the galvanometer.

Answer 1

Definition of Wheatstone Bridge:
A Wheatstone bridge is a circuit used to measure unknown resistances. It consists of four resistors arranged in a diamond shape, with a galvanometer connected between two opposite nodes. Condition for Balance:
Let the resistances of the four arms of the Wheatstone bridge be $R_1$, $R_2$, $R_3$, and $R_4$. The bridge is balanced when no current flows through the galvanometer. This occurs when: \[ \frac{R_1}{R_2} = \frac{R_3}{R_4}. \] Derivation:
At balance, the potentials at the two points connected to the galvanometer are equal. Using Ohm's law: \[ \frac{V_{AB}}{R_1} = \frac{V_{AD}}{R_2}, \quad \frac{V_{AB}}{R_3} = \frac{V_{AD}}{R_4}. \] Simplify: \[ \frac{R_1}{R_2} = \frac{R_3}{R_4}. \] Thus, the condition for the Wheatstone bridge to be balanced is: \[ \boxed{\frac{R_1}{R_2} = \frac{R_3}{R_4}}. \]