Wheatstone BridgeJEE Main

Concept

Four resistors in a diamond with a galvanometer across the middle. When the two voltage dividers produce equal potentials, no current crosses — the bridge is balanced and $P/Q = R/S$. This null method measures resistance precisely because zero-detection is immune to battery drift and meter calibration.

Key formula

Derivation

With no galvanometer current, arms P–Q and R–S are independent dividers: $V_B = \varepsilon\frac{Q}{P+Q}$, $V_D = \varepsilon\frac{S}{R+S}$.

Setting $V_B = V_D$ and cross-multiplying gives $PS = QR$. When unbalanced, replace the bridge by its Thevenin equivalent to get the galvanometer current.

Scenarios to explore

• Wheatstone Bridge — Null method — balance P/Q = R/S for precision resistance.

Real-world applications

• The meter bridge is a Wheatstone bridge with a 1 m wire as P–Q.
• Strain gauges & RTD thermometers sit in bridge arms — tiny ΔR becomes measurable ΔV.
• Carey Foster bridge for nearly equal resistances.

JEE exam tips

• Balanced ⇒ delete the galvanometer branch; the network reduces to (P+Q)∥(R+S).
• Interchanging battery and galvanometer preserves the balance condition.
• Sensitivity is best when all four arms are comparable in magnitude.

Common mistakes

• P/Q = S/R (inverted ratio) — keep arms on the same side of the galvanometer together.
• Thinking balance depends on EMF or galvanometer resistance — it doesn't.
• Series/parallel reduction of a balanced bridge: the middle resistor can simply be REMOVED.

Exam traps to avoid

• Bridge balance is unaffected by adding resistance in series with the battery or galvanometer.
• In an unbalanced bridge, current through the galvanometer needs Thevenin/Kirchhoff — no shortcut.