Wheatstone Bridge Questions

What is Wheatstone Bridge?

Wheatstone bridge, also known as the resistance bridge, is the setup that is used for measuring the unknown resistance. It was invented by Samuel Hunter Christie in 1833 and was later popularised by Sir Charles Wheatstone in 1843.

A Wheatstone bridge comprises four arms which are termed as resistors, and among which the ratio of two resistors is kept at a fixed value and the two arms left, that is, the remaining arms are balanced, one of them can be varied while the other arm is an unknown resistor.

Then through the method of balancing or null condition, the unknown resistance is calculated. The circuit of the Wheatstone bridge provides the exact measurement of the resistance. There are many variations of the Wheatstone bridge that are utilised for the AC circuits.

Principle of Wheatstone Bridge

The working of a Wheatstone bridge is based on the principle of null deflection, which means that the ratio of their resistances is equal, and no current flows through the circuit. The Wheatstone bridge consists of a circuit of four resistors P, Q, R, S arranged as a quadrilateral abcd. Points a and c are linked to battery E, and b and d points are linked to the galvanometer G. The resistances are carefully chosen in such a way that the galvanometer shows zero deflection or current Ig through It is 0. This condition is fundamentally termed as the balanced condition of a bridge or null condition.

This is the condition when no current flows through the galvanometer, and it can be achieved by regulating the variable resistance and known resistance.

For this condition,

PS = RQ

Where, R is the unknown resistance, P and Q are the ratio arm of the bridge, and S is the standard arm of the bridge.

= R = (P/Q) x S

and then S is adjusted to the value where the null condition is met.

Derivation of Wheatstone Bridge

As we can see in the figure, the current arrives at the galvanometer and divides itself into two equal currents, that is I₁ and I₂.

Therefore, when the current through a galvanometer is zero, the following condition occurs,

I₁P=I₂R……… (1)

In a balanced condition, the current in the bridge is expressed as follows:

I₁=I₃ = E/(P+Q)

I₂=I₄= E/(R+S)

Here, the emf of the battery is E

The value of I₁ and I₂ after replacing in equation (1), we get

= RE/(R+S) = PE/(P+Q)

= P(R+S) = R(P+Q)

= PR+PS = RP+RQ

Hence, PS=RQ……… (2)

R=(P/Q) ×S………. (3)

Here, the balanced or null condition of the bridge is shown by equation (2) and the value of the unknown resistance is determined by equation (3). Also, R is the unknown resistance, P and Q are the ratio arm of the bridge, and S is the standard arm of the bridge, and then S is adjusted to the value where the null condition is met.

Important Questions on Wheatstone Bridge

1) What are the applications of a Wheatstone bridge?

Following are the applications of a Wheatstone bridge –

• Measurement of low resistance by means of direct application of Ohm’s law can’t be done accurately. Therefore, in such cases, Wheatstone bridge circuits can be installed for accurate measurements.
• Some materials like semiconductors tend to vary resistance with the temperature, and as compared to ordinary resistors, these variations are huge. These materials are recognized as thermistors. A minor change in temperatures can be measured using thermistors for the Wheatstone bridge arrangement.
• Wheatstone bridge circuit helps to measure the changes in the intensity of light using the replacement of an unknown resistor with a photoresistor. The photoresistor functions on the basis of incident light.
• Wheatstone bridge is helpful in measuring strain and pressure.

2) What are the limitations of the Wheatstone Bridge?

• The Wheatstone bridge is a very sensitive device; therefore, it is possible that the measurements using a Wheatstone bridge may not be precise in an off-balance condition.
• Wheatstone bridge usually measures resistances that are in limited ranges from a ohms to kilo-ohms which means that for high resistance measurements, the galvanometer is insensitive to imbalance.
• The other drawback is that, due to the heating effect of the current through the resistance, the value of resistance changes; therefore, extreme current may even cause a permanent change in the value of resistance.
• If the four resistances are not comparable, the sensitivity of the circuit reduces.

3) A Wheatstone bridge has four resistances 200Ω, 20Ω, 400Ω, and 40Ω. If the bridge is connected to a 1.5 V battery, calculate the currents through individual resistors.

First arm resistance P=200Ω

Second arm resistance Q=20Ω

Third arm resistance R=400Ω

Fourth arm resistance S=40Ω

The potential difference is VAC =1.5V since points A and C are connected to the battery.

Therefore, the ratios of the arms,

P/Q=200/20 = 10

R/S= 400/40 = 10

Hence it satisfies the null condition that is, P/Q = R/S

∴ Current in the resistance P = current in the resistance V_AB/(P+Q)

That is, 1.5/ (200+20) = 0.0681A

Again, current in the resistance R = current in the resistance V_AB/(R+S)

That is, 1.5/ (400+40) = 0.0340A

4) Resistances of the ratio arms of a Wheatstone bridge are 300 Ω and 30Ω. The fourth arm is connected to an unknown resistor. Find the value of the unknown resistance if the third arm has a resistance of 250Ω in a balanced condition?

First arm resistance P=300Ω

Second arm resistance Q=30Ω

Third arm resistance R=250Ω

Let the unknown resistance be X, the ratio of resistances in the balanced condition will be, R/X=P/Q

X=(Q/P)

Substituting the values,

X= (30/300)250Ω

X= 25Ω

5) What is the principle of the Wheatstone bridge?

The working of a Wheatstone bridge is based on the principle of null deflection, which means that the ratio of their resistances is equal, and no current flows through the circuit.

6) Name the instrument that is used as a null detector in the Wheatstone bridge.

a) Galvanometer

b) Ammeter

c) Voltmeter

d) Multimeter

Correct Option: (a)

Explanation: A galvanometer is a sensitive device used for measuring the current, and also it determines the voltage between any two points of a circuit; therefore, it can detect even minor currents. Hence, a galvanometer is used as the null detector in a Wheatstone bridge, where the null point is a condition in which zero current flows through the circuit.

7) Which among the following is a false statement?

a) A galvanometer is used as the null detector in a Wheatstone bridge

b) A galvanometer is an ammeter with low resistance in series

c) Wheatstone bridge is susceptible to high dc current

d) Due to the errors introduced in contact resistance, a Wheatstone bridge cannot be used for accurate measurement

Correct Option: (c)

Explanation: A Wheatstone bridge is not susceptible to high dc current, but if not balanced, it can give inaccurate readings.

8) Which among the following ratios defines the sensitivity of a galvanometer?

a) Deflection in the galvanometer to the unit change in unknown resistance

b) Unit change in unknown resistance to thrice the deflection in the galvanometer

c) Half the unit change in unknown resistance to the deflection in the galvanometer

d) Deflection in the galvanometer to twice the unit change in unknown resistance

Correct Option: (a)

Explanation: The sensitivity of a galvanometer is defined as the ratio of deflection in the galvanometer to the unit change in unknown resistance. By increasing the number of turns, the sensitivity of a galvanometer can be increased by using a strong magnet or increasing the area of the coil.

9) PR = QS is the equation of a balanced Wheatstone bridge. Is it true or false?

a) True

b) False

Correct Option: (b)

Explanation: A Wheatstone bridge comprises four arms which are termed as resistors and among which the ratio of two resistors is kept at a fixed value and the other two resistors or arms are left without any fixed value, that is, the remaining arms are balanced, among which one of them can be varied while the other arm left is the resistor of unknown value. Where R is the unknown resistance, P and Q are the ratio arm of the bridge, and S is the standard arm of the bridge and is varied until the galvanometer shows null deflection, whereas P and Q are fixed. So, the equation is P/Q=R/S → PS = QR.

10) When does a Wheatstone Bridge is said to be unbalanced?

Under normal conditions, when the current flows through the galvanometer bridge is in an unbalanced condition.

Practice Questions

1. What is a Wheatstone bridge?
2. Explain the working of a Wheatstone bridge.
3. When is the Wheatstone bridge balanced?
4. What is the null condition in a Wheatstone bridge?
5. What is the difference between a galvanometer and an ammeter?

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