📌 1. Question Description
Wheatstone Bridge & Meter Bridge
The Wheatstone bridge is an electrical network used to determine an
unknown resistance by comparing it with known resistances.
It consists of four resistances arranged in the form of a bridge and a
galvanometer connected between the two junctions.
When the bridge is balanced, no current flows through the galvanometer.
The balanced condition provides a relation between the four resistances.
P/Q = R/S
The meter bridge is a practical form of the Wheatstone bridge in which a
uniform resistance wire of length 1 metre is used to determine an unknown
resistance.
X/R = l/(100-l)
🔌 2. What is a Wheatstone Bridge?
A Wheatstone bridge is an arrangement of four resistances used for
accurate measurement of an unknown resistance.
Resistance P
Known resistance in one arm.
Resistance Q
Known resistance in second arm.
Resistance R
Known or adjustable resistance.
Resistance S
Unknown resistance to be determined.
⚖️ 3. Balanced Condition
At balance, the galvanometer shows zero deflection.
Therefore, no current flows through the galvanometer.
Ig = 0
The potential of the two galvanometer junctions becomes equal.
Therefore:
P/Q = R/S
or
PS = QR
If S is unknown:
S = QR/P
📐 4. Derivation of Balanced Wheatstone Bridge
Let currents through the two branches be I₁ and I₂.
At balance, galvanometer current is zero.
Ig = 0
Therefore, the potential drop across P is equal to the potential drop
across the corresponding section of the other branch.
Using Ohm's law:
V = IR
The ratio of potential drops gives:
P/Q = R/S
Hence:
PS = QR
This is the
balanced condition of Wheatstone bridge.
🔬 5. Animated Wheatstone Bridge Practical
P/Q =
0.500
R/S =
0.500
Difference =
0.000
Galvanometer:
BALANCED — ZERO DEFLECTION ✔
📏 6. Meter Bridge
A meter bridge is a practical application of the Wheatstone bridge.
It consists of a 1 m long uniform resistance wire.
Total wire length = 100 cm
If X is an unknown resistance and R is a known resistance, and the
balance point is at distance l from the end connected to X:
X/R = l/(100-l)
Therefore:
X = Rl/(100-l)
🔬 7. Interactive Meter Bridge
1 Metre Resistance Wire
0 cm
100 cm
Known Resistance R:
5.00 Ω
Balance Length:
60.00 cm
Unknown Resistance X:
7.50 Ω
Ratio:
1.500
⭐ 8. Important Conditions for Meter Bridge
✔ Uniform Wire
The bridge wire should be uniform in cross-sectional area and material.
✔ Balance Point
The balance point should preferably lie near the middle of the wire.
✔ Clean Contacts
The jockey should make proper electrical contact with the wire.
✔ Low Resistance Connections
Connecting wires should have negligible resistance.
🚀 9. Advantages of Wheatstone Bridge
- Accurate measurement of resistance.
- Useful for detecting very small changes in resistance.
- Null method gives high accuracy.
- Used in electrical and electronic measuring instruments.
- Basis of strain-gauge and sensor circuits.
📝 10. MCQ Practice
1. A Wheatstone bridge is balanced when:
A. P + Q = R + S
B. P/Q = R/S
C. P/R = Q/S
D. P + R = Q + S
✔ Answer: B
2. In a balanced Wheatstone bridge, current through the galvanometer is:
A. Maximum
B. Minimum but non-zero
C. Zero
D. Infinite
✔ Answer: C
3. Meter bridge is based on:
A. Ohm's law
B. Coulomb's law
C. Wheatstone bridge principle
D. Faraday's law
✔ Answer: C
4. The total length of meter bridge wire is:
A. 10 cm
B. 50 cm
C. 100 cm
D. 200 cm
✔ Answer: C
5. If balance point is at 50 cm, the two wire resistances are:
A. Equal
B. Unequal
C. Zero
D. Infinite
✔ Answer: A
6. At balance point, galvanometer shows:
A. Maximum deflection
B. Zero deflection
C. Constant current
D. Infinite current
✔ Answer: B
7. Meter bridge formula for unknown resistance X is:
A. X = R(100-l)/l
B. X = Rl/(100-l)
C. X = R+l
D. X = R/l
✔ Answer: B
8. For maximum accuracy, the balance point should preferably be:
A. Near 0 cm
B. Near 10 cm
C. Near 50 cm
D. Near 100 cm
✔ Answer: C
9. Wheatstone bridge works on the:
A. Null method
B. Heating effect
C. Magnetic effect
D. Chemical effect
✔ Answer: A
10. If P = 2Ω, Q = 4Ω and R = 3Ω, balanced S is:
A. 1.5Ω
B. 3Ω
C. 6Ω
D. 8Ω
✔ Answer: C
🟣 11. Assertion–Reason Practice — 5 Questions
Choose the correct option:
A. Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
B. Both Assertion and Reason are true, but Reason is not the correct explanation of Assertion.
C. Assertion is true, but Reason is false.
D. Assertion is false, but Reason is true.
Assertion (A):
A Wheatstone bridge is balanced when no current flows through the
galvanometer.
Reason (R):
At balance, the potential difference between the two junctions connected
to the galvanometer is zero.
Answer: A
Explanation: Equal potentials at the two galvanometer junctions
produce zero potential difference and hence zero galvanometer current.
Assertion (A):
The balanced condition of a Wheatstone bridge is P/Q = R/S.
Reason (R):
At balance, the potential of the two junctions connected to the
galvanometer is equal.
Answer: A
Explanation: Equal junction potentials lead to the resistance-ratio
condition P/Q = R/S.
Assertion (A):
A meter bridge is a practical application of the Wheatstone bridge.
Reason (R):
A meter bridge uses a uniform resistance wire whose resistance is
proportional to its length.
Answer: A
Explanation: The uniform wire provides resistance ratios according
to the corresponding lengths, making the Wheatstone principle practical.
Assertion (A):
For greater accuracy, the balance point in a meter bridge should be close
to 50 cm.
Reason (R):
Near the middle of the wire, small errors in measuring the balance length
have a relatively smaller effect on the calculated resistance.
Answer: A
Explanation: A balance point near the middle gives a more favourable
ratio and reduces the percentage error.
Assertion (A):
If the galvanometer shows zero deflection, the current through the entire
Wheatstone bridge is zero.
Reason (R):
At balance, only the current through the galvanometer branch is zero.
Answer: D
Explanation: Galvanometer current is zero, but current can still
flow through the other branches of the bridge.
🟢 12. 2 Marks — 6 Questions
Q1
What is a Wheatstone bridge?
Q2
State the balanced condition of a Wheatstone bridge.
Q3
What happens to galvanometer current at balance?
Q4
What is a meter bridge?
Q5
Write the formula used to determine unknown resistance using a meter bridge.
Q6
Why is a meter bridge wire made uniform?
🟡 13. 3 Marks — 6 Questions
Q1
Explain the balanced condition of a Wheatstone bridge.
Q2
Explain why the galvanometer shows zero deflection at balance.
Q3
Derive the relation P/Q = R/S for a balanced Wheatstone bridge.
Q4
Explain the principle of a meter bridge.
Q5
Why should the balance point of a meter bridge preferably lie near 50 cm?
Q6
A meter bridge has R = 5Ω and balance length 60 cm. Calculate X.
🟠 14. 4 Marks — 6 Questions
Q1
Derive the balanced condition of a Wheatstone bridge using Kirchhoff's laws.
Q2
Explain the construction and working of a meter bridge.
Q3
Derive X = Rl/(100-l) for a meter bridge.
Q4
A Wheatstone bridge has P = 2Ω, Q = 4Ω and R = 3Ω. Find the value of S for balance.
Q5
A meter bridge has a resistance of 6Ω in the right gap and balance point at 40 cm. Find the resistance in the left gap.
Q6
Discuss four precautions to obtain accurate results in a meter bridge experiment.
🔴 15. 5 Marks — 6 Questions
Q1
Derive the balanced condition of Wheatstone bridge using Kirchhoff's laws.
Q2
Explain the working of a meter bridge and derive the expression for unknown resistance.
Q3
Explain the relation between Wheatstone bridge and meter bridge.
Q4
Explain the role of galvanometer and jockey in a meter bridge experiment.
Q5
A resistance X is connected in one gap of a meter bridge and 4Ω in the other. The balance point is at 60 cm. Calculate X.
Q6
Explain the major sources of error in a meter bridge experiment and methods to minimise them.
🔵 16. 6 Marks — 6 Questions
Q1
Derive the balanced condition of a Wheatstone bridge in detail using
Kirchhoff's laws and explain its physical meaning.
Q2
Describe the construction, principle and working of a meter bridge.
Derive the formula used for determining an unknown resistance.
Q3
Explain how a meter bridge is obtained from a Wheatstone bridge and derive
the resistance-length relation.
Q4
A meter bridge has an unknown resistance X in the left gap and 5Ω in the
right gap. The balance point is at 40 cm. Calculate X and explain the
procedure.
Q5
Explain the complete experimental procedure for determining an unknown
resistance using a meter bridge, including precautions.
Q6
Discuss the principle, derivation, applications, limitations and sources
of error of the Wheatstone bridge and meter bridge.
🧮 17. Numerical Practice
Example 1 — Wheatstone Bridge
P = 2Ω, Q = 4Ω and R = 3Ω. Find S for a balanced bridge.
P/Q = R/S
2/4 = 3/S
S = 6Ω
✔ Answer: S = 6Ω
Example 2 — Meter Bridge
A known resistance of 5Ω is connected in the right gap of a meter bridge.
The balance point is at 60 cm from the left end. Find the unknown resistance
in the left gap.
X/R = l/(100-l)
X/5 = 60/40
X = 7.5Ω
✔ Answer: X = 7.5Ω
🚀 18. Quick Revision
Wheatstone Bridge:
Used to determine unknown resistance.
Balanced condition:
P/Q = R/S
At balance:
Ig = 0
Meter Bridge:
Practical application of Wheatstone bridge.
Meter bridge equation:
X/R = l/(100-l)
Unknown resistance:
X = Rl/(100-l)
Best balance point:
Near 50 cm.
Important principle:
Resistance of a uniform wire is proportional to its length.
