A Wheatstone Bridge is a basic electrical circuit that measures the unknown resistances with high accuracy. It contains four resistors arranged in a rhombus and between two of its opposite corners, there is a galvanometer connected. In case the bridge is balanced, the proportion of two known resistors equals the ratio of the other two resistors which helps calculate the unknown resistance.
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In this article, we will discuss the concept of Wheatstone's Bridge. It is important for class 12 and competitive examinations such as NEET, and JEE Main where Wheatstone Bridge not only illustrates electrical resistance principles and circuit analysis but also forms a basis for more advanced topics regarding electronics and instrumentation. Over the last ten years of the JEE Main exam (from 2013 to 2023), a total of ten questions have been asked on this concept. And for NEET two questions were asked from this concept.
It is an arrangement of four resistances which can be used to measure one of them in terms of rest. Let R is an adjustable resistance, Pand Q are known resistance and S is an unknown resistance. To obtain valur of S we will close the keys K1 and K2 and will adjust R to obtain null deflection in the galvanometer. Then the balancing condition of bridge is
PQ=RSVB=VD
(Balanced condition)
No current will flow through the galvanometer
unbalanced condition: VB>VD
(VA−VB)<(VA−VD)
Current will flow from A to B
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Wheatstone bridge derivation
The Wheatstone bridge circuit is seen in the diagram above. R1, R2, R3, and Rx are four resistors placed in a quadrilateral ABCD pattern. Through the key K1, the points A and B are connected to a battery E.
Through the key K2, the points B and D are connected to a galvanometer G.
The resistances are chosen in such a way that the galvanometer needle does not deflect and the current IG. flowing through it is zero. This is referred to as the bridge's null condition or balanced condition. R1/R2 Equals R/S in this situation.
Instead of S, an unknown resistor is attached, and the resistor R can be changed. The ratio arms are sometimes referred to as the resistors R1 and R2. The R1/R2 ratio is kept constant, and R is set to a value that meets the null condition. The unknown resistance comes from,
(R2.R1)/R3=Rx
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Some important points-
Example 1: In a Wheatstone’s bridge, three resistances P, Q and R, are connected in the three arms and the fourth arm is formed by two resistances S1 and S2 connected in parallel. The condition for the bridge to be balanced will be
1) PQ=RS1+S2
2) PQ=2RS1+S2
3) PQ=R(S1+S2)S1S2
4) PQ=R(S1+S2)2S1S2
Solution
Wheat stone Bridge
It is an arrangement of four resistances which can be used to measure one of them in terms of rest
wherein
We know that PQ=RS
$$
\begin{aligned}
& \because S=\frac{S_1 S_2}{S_1+S_2} \
& \therefore \frac{P}{Q}=\frac{R\left(S_1+S_2\right)}{S_1 S_2}
\end{aligned}
$$
Example 2: The current I drew from the 5-volt source will be :
1) 0.17 A
2) 0.33 A
3) 0.5 A
4) 0.67 A
Solution:
Wheat stone Bridge
It is an arrangement of four resistances which can be used to measure one of them in terms of rest
wherein
We know that PQ=RS
The equivalent circuit is a balanced Wheatstone's bridge. Hence no current flows through arm BD here PQ=RS⇒510=1020
AB and BC are in a series
$$
\therefore R_{A B C}=5+10=15 \Omega
$$
AD and AC are in series
$$
\therefore R_{A D C}=10+20=30 \Omega
$$
ABC and ADC are in paralle
$$
\begin{aligned}
& \therefore R_{e q}=\frac{\left(R_{A B C}\right)\left(R_{A D C}\right)}{\left(R_{A B C}+R_{A D C}\right)} \
& \text { or } \quad R_{e q}=\frac{15 \times 30}{15+30}=\frac{15 \times 30}{45}=10 \Omega \
& \therefore \text { Current } I=\frac{E}{R_{e q}}=\frac{5}{10}=0.5 \mathrm{~A}
\end{aligned}
$$
Example 3: In a metre bridge experiment, the null point is obtained at 20 cm from one end of the wire when resistance X is balanced against another resistance Y . If X<Y, then where will be the new position (in cm) of the null point from the same end, if one decides to balance a resistance of 4X against Y?
1) 50
2) 80
3) 40
4) 70
Solution:
Wheat stone Bridge
It is an arrangement of four resistances which can be used to measure one of them in terms of rest
wherein
$$
\frac{R_1}{R_1}=\frac{l_1}{l_2}=\frac{l_1}{\left(100-l_1\right)}
$$
In the first case, xy=20100−20=2080=14
In the second case, 4xy=l100−l=44=l100−l
$$
l=50 \mathrm{~cm}
$$
Example 4: Four resistances of 15Ω,12Ω,4Ω and 10Ω respectively in cyclic order to form Wheatstone's network. The resistance that is to be connected in parallel with the resistance of 10Ω to balance the network is Ω⋅
1) 10
2) 5
3) 15
4) 20
Solution:
For a balanced Wheatstone bridge R1R2=R3R4 or R1R3=R2R4 R2=12Ω and R4=4Ω
As R2R4=124=3
So using R1=15Ω
We get R3=RAD=5Ω
let us connect x-ohms in parallel to the 10 -ohm resistance
i.e R3=5Ω=x∗10x+10
we get x=10Ω
So the answer will be 10.
Example 5: The Wheatstone bridge shown in the figure here gets balanced when the carbon resistor used as R1 has the colour code (Orange, Red, Brown) The resistors R2 and R4 are 80 and 40, respectively. Assuming that the colour code for the carbon resistors gives their accurate values, the colour code for the carbon resistor, used as R3 , would be :
1) Brown, Blue, Brown
2) Brown, Blue, Black
3) Red, Green, Brown
4) Grey, Black, Brown
Solution:
For a balanced Wheatstone network,
$$
\begin{aligned}
& \frac{R_1}{R_3}=\frac{R_2}{R_4} \
& \frac{R_1}{R_3}=\frac{80}{40}=2 \
& \therefore R_1=2 R_3
\end{aligned}
$$
For R1 which has the colour code (Orange, Red, and Brown)
$$
\begin{aligned}
& R_1=32 \times 10=320 \
& \therefore R_3=160
\end{aligned}
$$
where 1 - brown
6 - blue
0 -black
Wheatstone bridge method for measuring an unknown resistance has the following merits over the other methods for measuring the resistance. It has a null method therefore, the measurement of resistance made by this method is not affected by the internal resistance of the battery used. As the measurement of current or potential difference is involved, the measurements are not affected because of the fact that the ammeters and voltmeters are not ideal ones.
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NCERT Physics Notes:
The Wheatstone bridge operates on the null deflection principle, which states that their resistance ratios are equivalent and that no current flows across the circuit.
When no current passes through the galvanometer, the Wheatstone bridge is considered to be balanced. By modifying the known and variable resistances, this condition can be attained.
The bridge is unbalanced under normal conditions, with current flowing via the galvanometer.
The resistance of the leads and connections becomes significant when measuring low resistance, introducing an inaccuracy.
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