In 1843, Charles Wheatstone didn’t just build a bridge — he built one of the most powerful resistance-measurement tools in the history of electrical science. The Wheatstone bridge is an elegant four-resistor circuit that can determine an unknown resistance with extraordinary precision by exploiting a balanced null condition: when the bridge is balanced, no current flows through the galvanometer, and the ratio of resistances reveals the unknown value exactly.
The metre bridge is the practical, lab-friendly implementation of the Wheatstone bridge. Instead of four separate resistors, it uses a single 1-metre uniform resistance wire — the wire itself acts as two of the four resistors (the ratio arms), while the other two arms are a known resistance box and the unknown resistance. By sliding a jockey along the wire to find the balance point, students can determine any unknown resistance quickly, accurately, and repeatedly.
This guide covers both topics together as CBSE Class 12 teaches them: the Wheatstone bridge circuit, its derivation using Kirchhoff’s laws, the balanced bridge condition, the metre bridge as its practical form, construction and parts, the step-by-step experiment procedure, observation table, result calculation, sources of error, precautions, and uses. All apparatus described is manufactured and supplied by AJKANT Overseas from Ambala, India.
- 1. Wheatstone Bridge — Circuit and Working Principle
- 2. Derivation of Balanced Bridge Condition
- 3. Metre Bridge — Construction and Parts
- 4. Metre Bridge Formula
- 5. Experiment Procedure — Step-by-Step
- 6. Observation Table
- 7. Sources of Error and Precautions
- 8. Uses of Wheatstone Bridge and Metre Bridge
- 9. Frequently Asked Questions (FAQ)
1. Wheatstone Bridge — Circuit and Working Principle
A Wheatstone bridge is a circuit consisting of four resistors arranged in a diamond (rhombus) shape, with a galvanometer connected between the two mid-points of the diamond, and a battery connected across the other two opposite mid-points. The circuit was originally designed by Samuel Hunter Christie (1833) and popularised by Sir Charles Wheatstone (1843).
📈 Wheatstone Bridge Circuit Diagram
How to read the circuit: Current from battery (+) at A splits at A: part goes through P to B, part goes through Q to D. Current from B splits: part through galvanometer G to D, part through R to C. Current from D goes through S to C. Both meet at C (battery −).
The bridge works on this key insight: when the bridge is balanced (Iᵒ = 0), points B and D are at exactly the same potential. If Vᵉ = Vᵈ, no current flows from B to D (or D to B) through the galvanometer. This zero-current condition gives a precise ratio relationship between the four resistors that is independent of the battery EMF.
2. Derivation of the Balanced Bridge Condition
At balance (galvanometer current Iᵒ = 0), current through P equals current through R (same branch), and current through Q equals current through S.
Let I₁ = current through P and R, and I₂ = current through Q and S.
- Potential drop across P: Vᵃ − Vᵉ = I₁ P
- Potential drop across Q: Vᵃ − Vᵈ = I₂ Q
- Since Vᵉ = Vᵈ (balance condition): I₁ P = I₂ Q …(1)
- Potential drop across R: Vᵉ − Vᵇ = I₁ R
- Potential drop across S: Vᵈ − Vᵇ = I₂ S
- Since Vᵉ = Vᵈ: I₁ R = I₂ S …(2)
Dividing equation (1) by equation (2):
Sensitivity: The bridge is most sensitive (gives the sharpest null point) when all four resistors are of equal or nearly equal value. The sensitivity decreases when the ratio P/Q is very large or very small.
3. Metre Bridge — Construction and Parts
The metre bridge is the simplest, most practical implementation of the Wheatstone bridge for school laboratory use. The four resistors P, Q, R, and S of the Wheatstone bridge are physically realised as:
- P = resistance of the wire from 0 to the balance point (length l cm)
- Q = resistance of the wire from balance point to 100 cm (length 100−l cm)
- R = known resistance from the resistance box
- S = unknown resistance coil
Since the wire is uniform: P/Q = l/(100−l). Therefore: S = R × (100−l) / l
4. Metre Bridge Formula
l = balance length from left end of wire (cm) | (100−l) = remaining wire length (cm)
Derivation: At balance in Wheatstone bridge: P/Q = R/S. For uniform wire: P = ρl/A and Q = ρ(100−l)/A, so P/Q = l/(100−l).
Therefore: l/(100−l) = R/S ⇒ S = R(100−l)/l
Worked Example: R = 10 Ω, balance length l = 40 cm.
S = 10 × (100−40)/40 = 10 × 60/40 = 15 Ω
Resistance from 2nd reading: S = R × l′/(100−l′)
Mean S: Average of the two values for greater accuracy.
5. Experiment Procedure — Step-by-Step
Aim: To find the unknown resistance using a metre bridge.
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Set Up the CircuitConnect the unknown resistance S to the left gap and the resistance box R to the right gap of the metre bridge. Connect the galvanometer between the jockey and the central terminal. Connect the battery with plug key K in series across the ends of the wire. Ensure all connections are tight, using clean wire ends free of insulation.
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Select a Suitable Value of RSet R in the resistance box to a value that gives a balance point l between 30 and 70 cm (ideally near 50 cm). Start with R = 10 Ω and observe the galvanometer deflection at the two ends of the wire. If both deflections are in the same direction, the balance point is outside the wire range — change R. If deflections are in opposite directions, a balance point exists somewhere on the wire.
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Find the Balance Point (Null Point)Close key K. Press the jockey gently at different points along the wire. Find the position l (in cm) where the galvanometer shows exactly zero deflection. Narrow down the position by pressing at nearby points until zero is confirmed. Note the balance length l carefully from the cm scale.
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Calculate Unknown Resistance SUsing the formula: S = R(100−l)/l. Calculate S for this reading and record in the observation table.
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Interchange R and S, Find New Balance Length l′Swap the positions of R (resistance box) and S (unknown coil). Find the new balance length l′. Calculate S = R × l′/(100−l′). This reading eliminates end errors. Record in the observation table.
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Repeat for Different Values of RChange R to 3–4 different values (e.g., R = 5, 10, 15, 20 Ω). For each R, find both l (direct) and l′ (interchanged), calculate S from both, and take the mean. Record all readings in the observation table. Take the mean of all S values as the final result.
6. Observation Table
Least count of metre bridge scale: 0.1 cm | Unknown Resistance S (approx.): _____ Ω
| S.No. | R (Ω) (Resistance Box) |
Balance length l (cm) (Direct) |
S = R(100−l)/l (Ω) |
Balance length l′ (cm) (Interchanged) |
S = Rl′/(100−l′) (Ω) |
Mean S (Ω) |
|---|---|---|---|---|---|---|
| 1 | ____ | ____ | ____ | ____ | ____ | ____ |
| 2 | ____ | ____ | ____ | ____ | ____ | ____ |
| 3 | ____ | ____ | ____ | ____ | ____ | ____ |
| 4 | ____ | ____ | ____ | ____ | ____ | ____ |
| Overall Mean S = | ____ Ω | |||||
ρ = S × A / L = S × (πr²) / L (where r = radius of wire, L = length of wire)
7. Sources of Error and Precautions
8. Uses of Wheatstone Bridge and Metre Bridge
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9. Frequently Asked Questions (FAQ)
A Wheatstone bridge is said to be balanced when no current flows through the galvanometer connected between the two mid-points of the diamond circuit. The balanced condition is: P/Q = R/S, or equivalently, PS = QR (cross-multiplication form). At balance, points B and D (mid-points) are at equal potential, so no current flows between them regardless of the galvanometer’s resistance. This condition is derived from Kirchhoff’s current and voltage laws applied to the bridge circuit and is independent of the battery EMF and internal resistance.
The formula for finding the unknown resistance S using a metre bridge is: S = R × (100−l) / l, where R is the known resistance from the resistance box (Ω) and l is the balance length (in cm) from the left end of the wire. This formula comes from the Wheatstone bridge balance condition P/Q = R/S, where P = resistance of wire of length l and Q = resistance of wire of length (100−l). Since the wire is uniform, P/Q = l/(100−l), giving S = R(100−l)/l. When R and S are interchanged, the formula becomes S = R × l′/(100−l′), where l′ is the new balance length.
The balance point should ideally be between 30 and 70 cm (near the centre of the wire) for maximum accuracy because: (1) Sensitivity is maximum near the centre: At l = 50 cm, the bridge is most sensitive (all four arms have equal resistance). A small change in resistance gives a large deflection. (2) Errors are minimised: Near the ends (l < 10 cm or l > 90 cm), small errors in reading l lead to large errors in the calculated value of S. For example, at l = 5 cm, an error of 0.5 cm in l causes a 10% error in S. At l = 50 cm, the same 0.5 cm error causes only 1% error. Adjust R to bring the balance point into the 30–70 cm range.
End errors in a metre bridge arise from two sources: (1) The resistance wire may not begin exactly at the 0 cm and end exactly at 100 cm marks — there may be small shifts due to the physical mounting of the wire. (2) The thick copper strips at the ends have their own (small but non-zero) resistance, which is not accounted for in the formula. These cause all balance length readings to be shifted by a constant amount, introducing a systematic error. They are eliminated by: taking two readings — one direct (balance length l with R in right gap and S in left gap) and one interchanged (balance length l′ with S in right gap and R in left gap). The mean of the two calculated S values cancels the end error.
Both the metre bridge and potentiometer use a uniform resistance wire as part of their circuit, but they serve different purposes and work on different principles: The metre bridge uses the Wheatstone bridge null principle to find unknown resistance — the wire provides ratio arms P and Q of the bridge, and balance occurs when P/Q = R/S. It measures resistance. The potentiometer uses the principle V ∝ l (potential difference proportional to length) to measure unknown EMF or terminal voltage by finding the null point (zero galvanometer deflection) — it measures voltage/EMF. In both cases, the galvanometer reads zero at the balance point, but what is being balanced is different: resistance ratio in the metre bridge, and voltage in the potentiometer.
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