A Wheatstone bridge is a circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component. The key to understanding a balanced Wheatstone bridge lies in recognizing that when the bridge is balanced, the ratio of the resistances in one leg is equal to the ratio of the resistances in the other leg. This allows us to calculate an unknown resistance if the other three resistances are known. When balanced, no current flows through the galvanometer (or the component connecting the two middle points), indicating that the potential difference between these points is zero.
The balancing condition is expressed as: $$\frac{R_1}{R_2} = \frac{R_3}{R_4}$$, where $R_1$, $R_2$, $R_3$, and $R_4$ are the resistances in the four arms of the bridge. If $R_4$ is the unknown resistance, it can be calculated as: $$R_4 = R_3 \cdot \frac{R_2}{R_1}$$.
Match the terms with their definitions:
| Term | Definition |
|---|---|
| 1. Galvanometer | A. A circuit used to measure an unknown resistance. |
| 2. Wheatstone Bridge | B. The state where no current flows through the galvanometer. |
| 3. Resistance | C. A device that detects small electric currents. |
| 4. Balanced Bridge | D. The opposition to the flow of electric current. |
| 5. Ratio | E. The quantitative relation between two amounts showing the number of times one value contains or is contained within the other. |
A Wheatstone bridge is in a __________ state when the __________ through the galvanometer is zero. In this condition, the __________ of the resistances in one leg is equal to the __________ of the resistances in the other leg. This principle is used to determine an __________ resistance.
Explain, in your own words, why a Wheatstone bridge is considered a null measurement device when it is balanced.
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