Wheatstone Bridge: The Wheatstone Bridge is also referred to as resistance bridge. Students can find the concept challenging because of the complexity present in the concept. However, this concept can be understood easily and within no time if extra determination and focus is given. Students need to grasp the basic concepts which will allow them to have a better understanding of Wheatstone bridge and what Wheatstone bridge is used to measure.

This article has provided an in-depth explanation about different aspects of Wheatstone bridge such as Wheatstone bridge formula, diagram, and so on. To know more about Wheatstone bridge, continue to read the article.

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Wheatstone Bridge: Details

A Wheatstone Bridge is basically an electrical circuit set up to compare resistances or measure the unknown value of a resistor’s resistance by creating a balance between the two legs of the bridge circuit. It is also known as a ‘resistance bridge’. It uses the comparison method to measure the value of unknown resistance.

The Wheatstone Bridge consists of four resistors put together in a  diamond-shaped circuit. Although initially developed to measure the value of unknown resistance, it can be used to calibrate measuring instruments like voltmeters, ammeters, etc., with the help of variable resistance and a simple mathematical formula. The Wheatstone bridge circuit gives the quite accurate value of measured resistance.

Wheatstone Bridge: Construction

It has four arms which consist of two known resistance, one variable resistance and one unknown resistance, the value of which has to be determined. The circuit includes an emf source and galvanometer. The basic circuit of the Wheatstone bridge is shown in the figure below.

The bridge has four resistors \({R_1},\,{R_2},\,{R_3}\) and \({R_4}.\) A source is connected across one pair of diagonally opposite points (\(A\) and \(C\) in the figure). \(AC\) is the battery arm. A galvanometer \(G\) (a device to detect currents) is connected between \(B\) and \(D.\) This line, shown as \(BD\) in the figure, is called the galvanometer arm. The electromotive source is connected between points \(A\) and \(C.\) The current that flows across the galvanometer is determined by the potential difference applied across it.

Wheatstone Bridge: Principles

A Wheatstone bridge is based on the principle of null deflection, i.e. when the ratio of resistances in the two arms is equal, no current flows will flow through the middle arm of the circuit. A galvanometer is connected in the middle arm, so when zero current passes through the galvanometer, then the bridge is said to be in a balanced condition. Therefore, in the balanced condition, the voltage difference between points \(B\) and \(D\) becomes zero, i.e., at both points voltage level would be at the same potential. This condition can be achieved by adjusting the known resistances \(P, Q\) and the variable resistance \(S.\) Although under normal conditions, the bridge remains unbalanced, i.e. some current flows through the galvanometer.

Wheatstone Bridge: Working

Consider the diagram of the Wheatstone bridge as shown below. It consists of four resistance \(P,\,Q,\,R\) and \(S\) with a battery of EMF \(E.\) Two keys \({K_1}\) and \({K_2}\) are connected across terminals A and C and B and D, respectively. First, connect the key \({K_1}\) and then press the key \({K_2}.\) Check if the galvanometer shows any deflection. If there is a deflection, adjust the value of variable resistance till the galvanometer gives a null deflection. When the galvanometer does not show any deflection, then the it is said to be balanced.

Since the galvanometer does not show any deflection, thus, no current is flowing through the galvanometer and terminals \(B\) and \(D\) are at the same potential. In this condition,
\(\frac{P}{Q} = \frac{R}{S}.\)

The arm containing resistors \(P\) and \(Q\) is sometimes referred to as the ratio arm. To find the value of unknown resistance, the resistor is connected in place of \(S,\) and \(R\)’s (the variable resistor) resistance is varied accordingly to achieve a null condition. Then, the value of unknown resistance can be given as:
\(S = \frac{Q}{P}R\)

The arms \(BD\) and \(AC\) are called conjugate arms of the bridge. This is because when the bridge is balanced, then interchanging the positions of the galvanometer and the battery; there is no effect on the balance of the bridge. The bridge is very reliable and gives an accurate result. The working of the bridge is similar to the potentiometer. We employ the concept for determining the medium-range resistance. Thus, this method is not suitable for the measurement of very low and very high resistance. Sensitive ammeters are used to measure high resistance.

Wheatstone Bridge: Derivation

When the Wheatstone bridge is balanced, no current flows through the galvanometer i.e. \({I_G} = 0.\) Thus, the current flowing across arms \(AB\) and \(AC\) will be \({I_1}\) and the current through arms \(AD\) and \(DC\) will be \({I_2}.\) According to Kirchhoff’s circuital law, the voltage drop across a closed loop is zero. Thus, applying Kirchhoff’s loop law across the loop \(ABDA,\) the sum of voltage drop along each arm of the loop will be zero. The potential across each resistor is equal to the product of its resistance and the current flowing through it, thus:
\({I_1}P – {I_2}R = 0\)
\(\frac{{{I_1}}}{{{I_2}}} = \frac{R}{P}\)……(i)
Similarly, applying Kirchhoff’s loop law across the loop \(CBDC,\) we get:
\({I_1}Q – {I_2}S = 0\)
\(\frac{{{I_1}}}{{{I_2}}} = \frac{S}{Q}\)….(ii)
From equations (i) and (ii), we get:
\(\frac{R}{P} = \frac{S}{Q}\)
Or \(\frac{P}{Q} = \frac{R}{S}\)
This is the condition for a balanced Wheatstone bridge.

Wheatstone Bridge Sensitivity

When we deal with measuring devices, sensitivity plays a major role in determining their usefulness. A more sensitive device is considered better and provides much more reliable results. When all the resistances are equal, or their ratio is equal to \(1,\) i.e. unity, such a Wheatstone bridge is more sensitive. For any value of this ratio, the sensitivity of the bridge decreases. This means that the bridge is the most accurate when the resistances are almost comparable.

Wheatstone Bridge: Applications

1. It is difficult to measure the resistance precisely, using ohm’s law. In any such circuit, an ammeter and voltmeter are attached across the unknown resistor to measure the current and voltage through it. But both these devices have their own limitations, leading to inaccurate results. Thus, the Wheatstone bridge can be used in such a circuit to measure precise results.

2. Materials like metals, semiconductors and insulators, all show different behaviour with the temperature variations. The changes in their temperature can be measured by using thermistors in the bridge circuit. A thermistor is a device whose resistance is temperature reliant.
3. We can measure strain and pressure using a Wheatstone bridge.

4. By replacing the unknown resistance with a photoresistor, the Wheatstone bridge can measure the variations in incident light.

Wheatstone Bridge: Errors

Following are the errors which can occur while measuring a value using the Wheatstone bridge.
1. The true value and the mentioned value of the resistance might be different, and this difference can cause a measurement error.
2. There might be inaccuracies in measurement due to less sensitivity of the galvanometer.
3. The self-heating of the bridge might alter its resistance and lead to an error in calculation.
4. The generation of thermal reasons can lead to errors in the measurement of low-value resistance.
5. Personal errors can occur when the person taking the reading is not being careful.

We can avoid the errors mentioned above by using the best qualities resistor and galvanometer. To minimise the error due to self-heating of resistance, we should measure the resistance quickly. By connecting a reversing switch between battery and bridge, thermal errors can be reduced.

Wheatstone Bridge: Limitations

When the bridge is in an unbalanced state, it gives inaccurate readings. We can use the the bridge to calculate the value of resistance from a few ohms to megaohms only. To measure any value lower or higher than this, the circuit needs to be modified. By applying a suitable emf, the upper range of the bridge can be increased, while By connecting lead at the binding post, the lower range can be improved.

Summary

Wheatstone bridge is a device that uses the comparison method to measure the value of minimum resistance. The value of this unknown resistance is calculated by comparing it with a known resistance. It has four arms which consist of two known resistance, one variable resistance and one unknown resistance, the value of which has to be determined.

The circuit includes an emf source and galvanometer. A Wheatstone bridge is based on the principle of null deflection, i.e. when the ratio of resistances in the two arms is equal, no current flows will flow through the galvanometer. This is the condition for a balanced Wheatstone bridge:\(\frac{P}{Q} = \frac{R}{S}\)

Frequently Asked Questions on Wheatstone Bridge

Frequently asked questions related to Wheatstone bridge is listed as follows:

Q. What is a balanced Wheatstone bridge?
Ans: A Wheatstone bridge is said to be balanced when no current flows through the galvanometer.

Q. What is the principle of the Wheatstone bridge?
Ans: A Wheatstone bridge works on the principle of null deflection. This means that no current will flow through the galvanometer when the ratio of resistances across the two arms is the same.

Q. What is a Wheatstone bridge?
Ans: A Wheatstone bridge is a simple electric circuit connected in the form of a quadrilateral with two known, one variable and one unknown resistance. By the method of null deflection, the unknown resistance precisely can be measured using a Wheatstone bridge.

Q. What are the uses of the Wheatstone bridge?
Ans: 1. Measure the value of unknown resistance
2. Compare the resistances of the given resistors
3. Measure strain or pressure
4. Measure the temperature changes in different materials

Q. Write the formula for the balanced condition in a Wheatstone bridge.
Ans: Let \(P,\,Q,\,R\) and \(S\) are the resistors connected in the bridge, then, the condition of a balanced Wheatstone bridge can be given as:
\(\frac{P}{Q} = \frac{R}{S}.\)

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