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An electric circuit is the path of the flow of electric current. Different components of an electric circuit are capacitors, resistors, wires, switches, and batteries. Circuit theory defines the techniques that describe this flow. The principle of circuit theory depends upon different laws and ideas, such as Kirchhoff’s law and Ohm’s law. These laws help evaluate the relationship between voltage, resistance and electric current.
According to Ohm’s law, the current flowing through any conductor will always be directly proportional to the voltage across two points. There are two laws of Kirchhoff, the first law is the Junction rule, and the second is the Voltage law.
The Wheatstone bridge is the set-up of four resistors, in which one resistor is unknown. This concept helps determine the unknown resistance as the ratio of these four resistors is constant. Let’s study the Wheatstone bridge derivation and Wheatstone bridge circuit in brief.
Circuit Theory
The circuit theory is based on two main laws: Ohm’s law and Kirchhoff’s Law. These laws are as follows:
Ohm’s Law
Ohm’s law is the first and one of the most important concepts that derive a relation between the voltage, current and resistance of any given electric circuit. According to this law, the amount of current flowing through any conductor at a given temperature will be directly proportional to the voltage across it.
The equation expressing the Ohm’s law is as follows:
E=IR
Here, E= Voltage
I=Current
R= Resistance
Kirchhoff’s Laws
Two laws of Kirchhoff’s define the circuit theory, these are as follows:
First Law of Kirchhoff or the Kirchhoff’s Current Law: This law of Kirchhoff defines the Conservation of Charge and can be represented with the following equation:
IENTERING+ IEXIT= 0
Second Law of Kirchhoff’s Kirchhoff’s Voltage Law: This law of Kirchhoff defines the Conservation of Energy and can be represented with the following equation:
∑∆V=0
∆V= Potential difference
Wheatstone Bridge
It is a device by which we determine the resistance of an unknown resistor. This Wheatstone bridge comprises four arms (the resistors). The ratio of any two resistors remains constant while the other two have to be balanced. One of these arms is unknown. By using the formula for the Wheatstone bridge, we can determine the resistance of this unknown resistor. Metre Bridge and Wien bridge are based on the principle of Wheatstone bridge.
Wheatstone Bridge Derivation
To get Wheatstone bridge derivation assumes a given Wheatstone bridge consisting of 4 resistances in an arm of a parallelogram (say ABCD). We use a cell in this arrangement.
On pressing a key (say k1), i Ampere current starts flowing through it. The current will further divide into two parts, i1 and i2, at a point (say A). The four resistances (say P, Q, R, and S) are arranged so that the bridge remains balanced on pressing the other key (say k2), which means there is no deflection in the arm of the galvanometer. When we press the other key, k2, there will be no current in the arm (say BD).
By Kirchhoff’s Voltage Law
In the given closed mesh, ABDA (half of the parallelogram),
-i1P +i2=0
i1P=i2R (Equation 1)
Similarly, in the other closed mesh BCDB,
i1Q=i2S (Equation 2)
On dividing the equations, we get,
P/Q= R/S
This equation is for a balanced Wheatstone bridge.
Solved Questions on Wheatstone Bridge
Q 1- In a given Wheatstone bridge, the resistance P is 10 Ω, Q is 100 Ω, and R is 20 Ω. Determine the value of S if the galvanometer shows zero deflection (balanced state).
Solution:
Using the formula of Wheatstone bridge as derived above:
P/Q= R/S
10/100= 20/S
=200 Ω
Answer: The value of S, when the Wheatstone bridge shows zero deflection, will be 200 Ω.
Q 2- Determine the value of ‘a’ for a given balanced Wheatstone bridge for which the values are as follows:
P= 400 Ω, Q= 800 Ω, R=a+200 and S=1000 Ω.
Solution:
Using the formula of Wheatstone bridge as derived above:
P/Q= R/S
400/800= a+200/1000
400 ×1000/800= a+200
a+200=500
a=500-200
a=300 Ω
Answer: The value of ‘a’ for a given balanced Wheatstone bridge is 300 Ω.
Q 3- Determine the value of S in a given Wheatstone bridge showing zero deflection with values P=100 Ω, Q=40 Ω and R=20 Ω.
Solution:
Using the formula of Wheatstone bridge:
P/Q= R/S
100/40=20/S
40×20/100=S
S=8 Ω.
Answer: The value of S in a given Wheatstone bridge showing zero deflection with values P=100 Ω, Q=40 Ω and R=20 Ω will be 8 Ω.
Conclusion
Circuit theory defines the flow of techniques of electric current in the given circuit. Ohm’s law and Kirchhoff’s laws are the basis of defining this circuit theory. These laws derive the relationship between resistance, electric current and voltage. The equation expressing Ohm’s law is E=IR.
The Wheatstone bridge, comprising four resistors, is used to determine the resistance of any unknown resistors. This Wheatstone bridge comprises four arms (the resistors). The ratio of any two resistors remains constant while the other two have to be balanced. P/Q=R/S equation is not for an unbalanced Wheatstone bridge.
