20.9 WHEATSTONE BRIDGE
20.9.1 Wheatstone Bridge
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| Figure 20.57 A Wheatstone bridge consisting of four resistors P, Q, R, and S connected in a bridge arrangement, with an additional resistor (or galvanometer) connected across points B and D. |
1 The circuit
(a) The Wheatstone bridge circuit consists of four resistors, P, Q, R and S connected in the manner as shown in Figure 20.57. Another resistor is connected across points B and D.
(b) Instead of a resistor, a galvanometer G may be connected across BD because G itself has resistance.
(c) A battery is connected across AC so that it can supply current to all the resistors.
(d) Normally one of the resistors, like S, is a variable resistor. The purpose of having a variable resistor in the circuit is to adjust its resistance so that a ‘balanced’ circuit can be obtained.
2 Condition for achieving a ‘balanced’ circuit
(a) In general, current flows through all the five resistors, i.e., P, Q, R, S and G. If we adjust the resistance of S, the current in each resistor will change.
(b) We could keep on adjusting the resistance of S so that the current flowing through the galvanometer G could be reduced to zero. When this condition (current through G = 0) is achieved, the circuit is said to be ‘balanced’.
3 Equation for balanced circuit
Suppose that no current flows through galvanometer G. Since no current flows through G, we would have the following conditions:
(a) The electric potential at point B must be equal to the electric potential at point D so that the p.d. across BD is zero. We get
p.d. across AB = p.d. across AD
p.d. across CB = p.d. across CD
(b) The current flowing through P must be equal to that flowing through Q. Let it be I1. Similarly, the current flowing through R must be equal to that flowing through S. Let it be I2.
Based on these two conditions, we get
I1P = I2R
I1Q = I2S
P / Q = R / S
We may also write the expression as
P / R = Q / S
EXAMPLE 20.19
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| Figure 20.58 A Wheatstone bridge used to determine the unknown resistance Q by adjusting resistors until the circuit is balanced under different conditions. |
Refer to the Wheatstone bridge circuit shown in Figure 20.58. The circuit is balanced when R = 100 Ω and S = 200 Ω. The resistance of Q is then changed to 250 Ω. The circuit is balanced again only when R has resistance 161 Ω. Determine the initial resistance of Q.
Answer
Since the circuit is balanced, we get
Q / P = 100 / 200
250 / P = 161 / 200
20.9.2 The Sliding Wire Bridge
1 Structure
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| Figure 20.59A sliding wire bridge setup, which is a form of Wheatstone bridge, consisting of a uniform wire, resistors, and a galvanometer used to measure unknown resistance. |
(a) Figure 20.59 shows the structure of a sliding wire bridge which is actually a Wheatstone bridge.
(b) Resistors or conductors having resistances R1 and R2 are connected across the air gaps.
(c) A bare uniform wire is connected across AB. The wire normally has a length of 1.0 m and resistance of several ohms.
(d) A galvanometer G is connected to the circuit in the manner as shown. The main function of G is to indicate whether there is any current flowing through it.
(e) A jockey is connected to G. It is made to slide on wire AB.
(f) The wire, resistors and galvanometer are connected to metal (normally copper) plates whose resistances are very low and may be neglected.
2 Principle
Suppose that when the jockey touches wire AB at point C, the galvanometer G indicates that there is no current flowing through it. This means that the circuit is balanced. Let the lengths of AC and CB be l1 and l2 respectively. Then we have
R1 / R2 = resistance of AC / resistance of CB
But, resistance of AC = rl1
resistance of CB = rl2
where r is the resistance per unit cm of wire AB and so is a constant. Hence we have
R1 / R2 = l1 / l2
If l1 and l2 are measured, and, say, R1 is known, then R2 can be determined. Hence, we can use this circuit to measure an unknown resistance whose value is not too low.
Note: This circuit is not suitable for measuring resistance whose value is 1 ohm or less.
Conclusion
The Wheatstone Bridge and Sliding Wire Bridge are important electrical circuits used for precise measurement of resistance. Both operate based on the principle of balance, where no current flows through the galvanometer, ensuring high accuracy.
The Wheatstone Bridge is highly effective for comparing and determining unknown resistances using the ratio of known resistors, while the Sliding Wire Bridge provides a practical method by relating resistance to the length of a uniform wire.
These methods are widely used in laboratories, education, and instrumentation due to their sensitivity, reliability, and ability to detect very small changes in resistance.
Overall, both bridges play a crucial role in electrical measurements and form the foundation for many modern sensing and measurement techniques.
Frequently Asked Questions (FAQ) – Application of Wheatstone Bridge & Sliding Wire Bridge
1. What is the main application of the Wheatstone bridge?
The main application is to measure unknown resistance accurately by balancing the bridge circuit.
2. Why is the Wheatstone bridge highly accurate?
It operates under a null condition where no current flows through the galvanometer, eliminating errors due to internal resistance.
3. Where is the Wheatstone bridge used in real life?
It is used in sensors such as strain gauges, thermistors, and light-dependent resistors (LDR) in industrial and scientific applications.
4. What is the use of a sliding wire bridge?
The sliding wire bridge is used to measure unknown resistance by comparing lengths along a uniform wire.
5. How does the sliding wire bridge improve measurement?
It provides a simple and practical way to determine resistance using proportional lengths, making it suitable for laboratory experiments.
6. Can these bridges detect small changes in resistance?
Yes, both are very sensitive and can detect very small variations in resistance.
7. Why are these bridges used in laboratories?
They are used for teaching and experiments because they provide accurate and reliable measurement methods.
8. What is the advantage of the sliding wire bridge over the Wheatstone bridge?
The sliding wire bridge is simpler to use and directly relates resistance to measurable wire length.
9. Are these bridges used in modern electronics?
Yes, especially the Wheatstone bridge, which is widely used in sensor circuits and measurement systems.
10. What condition is required for accurate measurement?
The circuit must be balanced so that no current flows through the galvanometer.
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