Application of Kirchhofs laws

1. GOVERNMENT COLLEGE OF ENGINEERING ,SALEM-11
DEPARTMENT OF MECHANICAL ENGINEERING
MECHANICAL-1
18ME503
INSTRUMENTATION AND QUALITY CONTROL
UNIT-2
SIGNAL CONDITIONING
WHEATSTONE BRIDGE

2. CONTENT:
 WHAT IS WHEATSTONE BRIDGE
 PRINCIPLE
 CONSTRUCTION & DERIVATION
 APPLICATION
 ADVANTAGES AND LIMITATIONS

3. WHAT IS WHEATSTONE BRIDGE
 Wheatstone bridge, also known as the resistance bridge. It is used to
calculate the unknown resistance of the circuit.
 It is invented by Samuel Hunter Christie in 1833, then later it is
popularized by Sir Charles Wheatstone in 1843.
 It is an important application of Kirchhoff's law.
 The Wheatstone Bridge Circuit comprises two known resistors, one
unknown resistor and one variable resistor connected in the form of a
bridge. This bridge is very reliable as it gives accurate measurements

4. KIRCHHOFF'S LAW
Kirchhoff's current law:
 Kirchhoff's current law states that the algebraic sum of the current meeting
at any junction in a circuit is zero.
 The convention is that , the current flowing
towards a junction is positive and the current
flowing away from the junction is negative .
I₁ + (-I₂) + (-I₃) + I₄ + I₅ =0
I₁ + I₄ + I₅ = I₂ + I₃
 The sum of the current entering the junction is
equal to the sum of the current leaving the junction.
This law is the consequence of conservation of charges.

5. KIRCHHOFF'S LAW
Kirchhoff’s voltage law:
Kirchhoff's voltage law states that the algebraic sum of the products of
resistance and current in each part of any closed circuit is equal to the
algebraic sum of the emf’s in that closed circuit. This law is a consequence
of conservation of energy
 In the closed loop ABCDEFA
I1R2 + I3R4 + I3r3 + I3R5 + I4R6 + I1r1 + I1R1 = E1 + E3
 For the closed loop ABEFA
I1R2 + I2R3 + I2r2 + I4R6 + I1r1 + I1R1 = E1 – E2
 As an illustration of application of Kirchhoff's second law, let us calculate
the current in the following networks.

6. PRINCIPLE
The Wheatstone bridge works on the principle of null
deflection, i.e. the ratio of their resistances are equal and no
current flows through the circuit. Under normal conditions,
the bridge is in the unbalanced condition where current flows
through the galvanometer. The bridge is said to be in a
balanced condition when no current flows through the
galvanometer. This condition can be achieved
by adjusting the known resistance and variable resistance.

7. CONSTRUCTION & DERIVATION
Wheatstone’s network consists of four resistances P, Q, R and S
connected to form a closed path. A cell of emf E is connected between
points A and C. The current I from the cell is divided into I1, I2, I3 and I4
across the four branches. The current through the galvanometer is Ig. The
resistance of galvanometer is G.

8. DERIVATION
Applying Kirchhoff's current law to junction B,
I1 – Ig – I3 = 0 ...(1)
Applying Kirchhoff's current law to junction D
I2 + Ig – I4 = 0 ...(2)
Applying Kirchhoff's voltage law to closed path ABDA
I1 P + IgG – I2 R = 0 ...(3)
Applying Kirchhoff's voltage law to closed path ABCDA
I1P + I3Q – I4S – I2R = 0 . ..(4)

9. DERIVATION
When the galvanometer shows zero deflection, the points B and D
are at same potential and Ig = 0. Substituting Ig = 0 in equation (1), (2) and
(3)
I1 = I3 ...(5)
I2 = I4 ...(6)
I1P = I2R ...(7)
Substituting the values of (5) and (6) in equation (4)
I1P + I1Q – I2S – I2R = 0
I1 (P + Q) = I2 (R+S) ...(8)
Dividing (8) by (7)
I1(P+Q) /I1P= I2(R+S) /I2R
P+Q/P = R+S/R

10. DERIVATION
1+Q/P = 1+S/R
Q/P = S/R
or P/Q = R/S
This is the condition for bridge balance. If P, Q and R are known,
the resistance S can be calculated.
APPLICATIONS
 The Wheatstone bridge is used for the precise measurement of low
resistance.
 Wheatstone bridge along with operational amplifier is used to measure
physical parameters such as temperature, light, and strain.
 Quantities such as impedance, inductance, and capacitance can be
measured using variations on the Wheatstone bridge.

11. ADVANTAGES AND LIMITATIONS
Advantages:
The main advantage in Wheatstone Bridge is that at null point
current does not flow in arm of the galvanometer, so no effect of the
resistance of galvanometer or no consumption of electric energy .
Limitations:
 For high resistance measurement, the measurement presented by the
bridge is so large that the galvanometer is insensitive to imbalance.
 The other drawback is the change in the resistance due to the heating
effect of the current through the resistance. Excessive current may even
cause a permanent change in the value of resistance

12. Thank you