Wheatstone bridge

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 I 1 R2 + I 3 R 4 + I 3 r 3 + I 3 R 5 + I 4 R 6 + I 1 r 1 + I 1 R 1 = E 1 + E 3 For the closed loop ABEFA I 1 R 2 + I 2 R 3 + I 2 r 2 + I 4 R 6 + I 1 r 1 + I 1 R 1 = E 1 – E 2 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 I 1 , I 2 , I 3 and I 4 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, I 1 – I g – I 3 = ...(1) Applying Kirchhoff's current law to junction D I 2 + Ig – I 4 = ...(2) Applying Kirchhoff's voltage law to closed path ABDA I 1 P + IgG – I 2 R = 0 ...( 3) Applying Kirchhoff's voltage law to closed path ABCDA I 1 P + I 3 Q – I 4 S – I 2 R = 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) I 1 = I 3 ...(5) I 2 = I 4 ...(6) I 1 P = I 2 R ...(7) Substituting the values of (5) and (6) in equation (4) I 1 P + I 1 Q – I 2 S – I 2 R = 0 I 1 (P + Q) = I 2 (R+S) ...( 8 ) Dividing (8) by (7) I 1 (P+Q) /I 1 P= I 2 (R+S) /I 2 R 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

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