In a balanced Wheatstone Bridge, R_1 = 10Omega, R_2 = 20Omega, and R_3 = 50Omega. What is the value of R_x?

100Omega Using R_1/R_2 = R_3/R_x, we get 10/20 = 50/R_x. Thus 0.5 = 50/R_x, so R_x = 100Omega.

Wheatstone Bridge Balance

Q: Why is the Wheatstone Bridge more accurate than using a simple voltmeter and ammeter to measure resistance?

Null measurement technique It is a "null" method. It doesn't depend on the accuracy of an ammeter reading a value, but rather on detecting the exact point where current is zero, which is much easier to measure precisely without being affected by the internal resistance of the meters.

Adjust four resistors and voltage source to balance a Wheatstone bridge. Galvanometer needle shows current; R₁/R₂ = R₃/Rx condition for zero deflection.

WHAT IS A WHEATSTONE BRIDGE?

A Wheatstone Bridge is a circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit. It consists of four resistors arranged in a diamond shape. When the bridge is **balanced**, the potential difference between the two midpoints is zero, and no current flows through the galvanometer connected between them. This allows for extremely precise resistance measurements.

HOW TO USE THIS VISUALIZATION

1. **Adjust the Known Resistors**: Change and until the galvanometer current reads zero. 2. **Observe the Balance**: Notice how the ratios of the arms must be equal for zero deflection: . 3. **Test Sensitivity**: See how a small change in the unknown resistor creates a measurable current in the central branch when the bridge is near balance.

CORE FORMULAS

Balance condition for the Wheatstone Bridge

Solving for unknown resistance

Condition for a balanced bridge

AP EXAM CONNECTION

Unit: Unit 4: Electric Circuits (Topic 4.3)
Learning Objective: LO 5.B.9

COMMON MISCONCEPTIONS

Current flows through the bridge at balance (no current flows through the central galvanometer branch)
Resistors must all be equal (only the ratios of the arms must be equal)

KEY TAKEAWAYS

At balance, the potential at both nodes of the galvanometer is the same.
The bridge allows measurement of resistance independent of the source voltage stability.
Sensitivity is highest when all four resistors have similar magnitudes.

PRACTICE QUESTIONS

Q1 (QUANTITATIVE): In a balanced Wheatstone Bridge, and . What is the value of ?

Show Answer & Explanation

Answer: 100Omega

Explanation: Using , we get . Thus , so .

Q2 (CONCEPTUAL): Why is the Wheatstone Bridge more accurate than using a simple voltmeter and ammeter to measure resistance?

Show Answer & Explanation

Answer: Null measurement technique

Explanation: It is a "null" method. It doesn't depend on the accuracy of an ammeter reading a value, but rather on detecting the exact point where current is zero, which is much easier to measure precisely without being affected by the internal resistance of the meters.