Determine Unknown Resistance Using Null Point Method
✅ FREE Experiment • 🔬 Interactive Bridge • 🎓 NEB Class 12 Physics
The Meter Bridge (also called Slide Wire Bridge) is a practical application of the Wheatstone Bridge principle. It's used to accurately measure unknown resistance by comparing it with a known standard resistance. The instrument consists of a one-meter long uniform resistance wire stretched between two copper strips, with resistances connected in gaps and a galvanometer detecting the null point.
When the bridge is balanced (null point), the ratio of resistances equals the ratio of corresponding wire lengths. This allows us to calculate an unknown resistance X from a known resistance R using the formula: X/R = l₁/l₂, where l₁ and l₂ are the lengths of wire segments.
Standard resistance (accurately known)
Resistance to be determined (hidden in real experiment)
Move along bridge wire to find null point
Where: X = unknown resistance, R = known resistance, l₁ = left wire length, l₂ = right wire length (100 - l₁)
Given: Known resistance R = 10 Ω, Meter bridge wire length = 100 cm
| S.No. | Normal Position (R in left gap, X in right gap) | Interchanged (X in left gap, R in right gap) | Mean X (Ω) |
||||
|---|---|---|---|---|---|---|---|
| Null Point l₁ (cm) |
l₂ = 100-l₁ (cm) |
X = R(l₁/l₂) (Ω) |
Null Point l₁' (cm) |
l₂' = 100-l₁' (cm) |
X = R(l₂'/l₁') (Ω) |
||
| No observations recorded yet. Click "Record" to add normal reading, then "Interchange R & X" and record again | |||||||
Final Result: Unknown resistance X = Calculate after recording observations
A Wheatstone bridge consists of four resistances arranged in a diamond shape with a galvanometer in the middle and a battery across opposite corners. The bridge is balanced (galvanometer shows zero deflection) when:
Or equivalently: P × S = Q × R
The meter bridge is a practical form of Wheatstone bridge where two resistances (P and Q) are replaced by segments of a uniform resistance wire. If the wire has uniform resistance per unit length, then resistances are proportional to lengths:
When known resistance R is in left gap and unknown resistance X is in right gap:
Or, since l₂ = 100 - l₁:
In the meter bridge:
The copper strips and connection points have some resistance (called end resistance or contact resistance). This introduces systematic error in measurements. To eliminate this error, we use the interchange method:
This method averages out the end resistance error because it affects both measurements in opposite ways, canceling out when we take the mean.
At the null point (balance point), the galvanometer shows zero deflection because:
The resistance wire must be uniform (constant diameter and resistivity). Non-uniform wire violates the assumption that resistance is proportional to length.
Copper strips, screws, and connections add extra resistance. Use interchange method to eliminate this systematic error.
More sensitive galvanometer detects smaller current differences, allowing more precise null point location. A sensitive galvanometer can detect deflection for 1-2 mm position change.
Should be sufficient to detect deflection but not too high (causes heating of wire and changes resistance). Typical: 2-4V with rheostat for current control.
Most accurate when null point is near the middle of wire (40-60 cm). Avoid positions near ends where percentage error in length measurement is higher.
The resistance of a uniform wire is given by:
Where:
For uniform wire, R ∝ l, which is the basis of the meter bridge.
Wheatstone bridge is an arrangement of four resistances in which when a specific condition is satisfied, no current flows through the galvanometer connecting the middle points. The balance condition is P/Q = R/S, or P×S = Q×R. This principle is used to measure unknown resistance accurately.
A meter bridge (or slide wire bridge) is a practical application of Wheatstone bridge where two resistances are replaced by segments of a one-meter long uniform resistance wire. It's used to determine unknown resistance by comparing it with a known standard resistance using the null point method.
At balance, Wheatstone condition gives: P/Q = R/X
For uniform wire: P ∝ l₁ and Q ∝ l₂
Therefore: P/Q = l₁/l₂
Combining: l₁/l₂ = R/X
Cross-multiplying: X × l₁ = R × l₂
Therefore: X = R × (l₂/l₁) or X = R × (100-l₁)/l₁
Null point (or balance point) is the position on the meter bridge wire where the galvanometer shows zero deflection. At this point, the potential at jockey equals the potential at galvanometer junction, so no current flows. It's detected by sliding the jockey along the wire until the galvanometer needle remains at zero position.
End resistance is the resistance of copper strips, screw contacts, and connection points at the ends of the meter bridge wire. It causes systematic error in measurements. We eliminate it using the interchange method: (1) Find null point with R in left gap, (2) Calculate X₁, (3) Interchange R and X positions, (4) Find new null point and calculate X₂, (5) Take mean: X = (X₁+X₂)/2. The end resistance errors cancel out in the mean.
The meter bridge formula X = R × (l₂/l₁) is based on the assumption that resistance is directly proportional to length. This is only true for uniform wire (constant cross-sectional area and resistivity throughout). Non-uniform wire would have variable resistance per unit length, making length measurements inaccurate for calculating resistance.
When null point is near the middle (around 50 cm), both l₁ and l₂ are comparable, giving maximum accuracy. Near the ends (say l₁ = 10 cm), a small error in length measurement causes large percentage error in the ratio l₁/l₂. For example, 1 cm error at l₁ = 10 cm gives 10% error, but same 1 cm error at l₁ = 50 cm gives only 2% error.
The galvanometer is a sensitive current detector used to identify the null point. When potentials at its two terminals are different, current flows and it shows deflection. When potentials are equal (balance condition), no current flows and it shows zero deflection. The more sensitive the galvanometer, the more accurately we can locate the null point.
Continuous current flow causes: (1) Joule heating of the resistance wire (I²R heating), which increases its temperature and resistance, changing the resistance-length relationship, (2) Battery drainage, (3) Thermal expansion of wire affecting its length, (4) All these factors introduce errors. The circuit should only be closed while taking readings.
Advantages: (1) No current at balance - measurement doesn't depend on battery voltage or internal resistance, (2) High accuracy - can measure resistances from milliohms to megaohms, (3) Null method - independent of meter calibration, only requires sensitive null detector, (4) Eliminates contact resistance when using interchange method.
No, not directly. The galvanometer is part of the bridge circuit and used for null detection. Its resistance doesn't appear in the balance equation because no current flows through it at balance. To measure galvanometer resistance, we would need to use it in one of the gaps and use a different null detector.
Reversing battery polarity reverses the current direction through the circuit, which reverses the galvanometer deflection direction for unbalanced conditions. However, the null point position remains the same because at balance, no current flows through the galvanometer regardless of polarity. The measurement is unaffected.
Constantan and manganin alloys have: (1) High resistivity - allows 1 meter length to have measurable resistance, (2) Low temperature coefficient - resistance doesn't change much with temperature, preventing errors from heating, (3) Uniform composition - ensures uniform resistance per unit length, (4) Mechanical strength - can be drawn into thin, uniform wire.
Both use Wheatstone bridge principle but differ in construction:
Meter Bridge: Two arms (P, Q) are wire segments with variable length ratio l₁/l₂.
Used to find unknown resistance.
Post Office Box: Has preset ratio arms (P/Q = 10/1, 100/1, etc.) and variable
standard resistance. More versatile - can measure wider range of resistances accurately.
Temperature changes affect: (1) Wire resistance - increases with temperature due to increased resistivity, (2) Wire length - thermal expansion changes l₁ and l₂, (3) Unknown resistance X - if it has high temperature coefficient. To minimize errors: work quickly, don't keep circuit closed long, use materials with low temperature coefficient, and work in stable temperature environment.