# Wheatstone Bridge Questions

By Varadi Hema|Updated : July 26th, 2022

Here we will briefly go through some Wheatstone bridge questions and their solutions. The Wheatstone bridge is an instrumental bridge used to measure the unknown resistance by the null detection technique.

The Wheatstone bridge consists of four resistors on four legs of the bridge, as shown below, and a Galvano meter for the null indication. The two legs consist of two known resistances. The remaining two legs consist of one unknown resistance and variable resistance to obtain the null indication.

At the null condition, the product of resistances of the opposite arms is equal.

R2R3=R1Rx

R2/R1=Rx/R3

## Wheatstone bridge questions 1

Four resistances, 4Ω, 8Ω, XΩ, and 6Ω, are connected in a series to form Wheatstone’s network. If the network is balanced, find the value of ‘X’.

1. 3 Ω
2. 5 Ω
3. 7 Ω
4. 10 Ω

Solution:

Given that,

R1=4Ω, R2=8Ω, R3=XΩ, R4=6Ω

at null condition,

R1/R3=R2/R4

4/X=8/6

⇒X=3Ω

Hence option A is the correct answer.

## Wheatstone bridge questions 2

In Wheatstone’s bridge arrangement PQRS, the ratio arms P and Q are nearly equal. The bridge is balanced when R = 700Ω. On interchanging P and Q, the value of R for balancing is 720Ω. Find the value of S.

1. 700 Ω
2. 720 Ω
3. 709.92 Ω
4. 705.75 Ω

Solution:

Given that, the ratio arms P and Q are nearly equal.

R = 700Ω

at null condition

P/Q=700/S ________(1)

P and Q are interchanged, and the bridge is balanced at R=510 Ω.
Q/P=720/S ________(2)

Multiply both equations to obtain the value of S.

1=700×720/S2

S=709.92 Ω

Hence option C is the correct answer.

## Wheatstone bridge questions 3

In the Wheatstone bridge given below, what should be the values of R1 and Rso that the bridge is balanced?

A) R1 = 6 ohms; R2 = any finite value
B) R1 = 6 ohms; R2 = 3 ohms
C) R1 = 29.4; R2 = 2 ohms
D) R1 = any finite value; R2 = 3 ohms

Answer: A. R1 = 6 ohms; R2 = any finite value

Solution:

In the given bridge circuit, if the outer bridge is balanced, then there is no current flow in the branch BD, and then R2 can be any finite value.

Hence, when the bridge is balanced.

21×10=R1×35

R1=210/35=6 Ohms

Hence option A is the correct answer.

## Wheatstone bridge questions 4

The four arms of a Wheatstone bridge are as follows: AB = 100 Ω, BC = 1000 Ω, CD = 4000 Ω, DA = 400 Ω. A galvanometer with an internal resistance of 100 Ω and a sensitivity of 10 mm/μA is connected between AC, while a battery of 4 V dc is connected between BD. Calculate the deflection if the resistance of arm DA is changed from 400 Ω to 401 Ω.

1. 20.4 mm
2. 40.8 mm
3. 2.04 mm
4. 4.08 mm

Solution:

Given the resistance of the arm, DA is changed to 401 Ω.

The given Wheatstone bridge can be drawn as shown below.

Deflection of galvanometer=(sensitivity)×(current flowing through Galvano meter)

We can use Thevenin’s theorem to find the current through the Galvano meter.

ID=VThRD+RTh

So to apply Thevenin’s theorem, remove the Galvanometer and assume that the branch AC is open-circuited.

VTh=VAC=VA-VC

VA=4×100/(401+100)=0.798 V

VC=4×1000/(4000+1000)=0.8 V

VTh=VAC=VA-VC=0.798-0.8=-0.002 V

While finding RTh, the Voltage source is replaced with a short circuit.

RTh=(401×100)/(401+100)+(4000×1000)/(4000+1000)=880.03

ID=VTh/(RD+RTh)=-0.002/(100+880.03)=-2.04 μA

The magnitude of ID=2.04 μA

Deflection of galvanometer =2.04×10-6×10×(10-3/10-6)=20.4 mm

Hence option A is the correct answer.

## Wheatstone bridge questions 5

Which instrument is used as the null detector in the Wheatstone bridge?
a) Voltmeter
b) Ammeter
c) Galvanometer
d) Multimeter

Option C

Explanation:

A galvanometer is used as a null detector in the Wheatstone bridge. When the bridge is balanced, the current through the galvanometer is zero. Due to its high sensitivity, the Galvano meter can sense the smallest values of currents.

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