Metrebridge

 Application of Wheatstone Bridge

A) Metrebridge : It is a device used to measure unknown resistance based on wheatstone network.The length of the wire is 1m, therefore it is called as metrebridge.

Construction : It consist of a uniform conductor of 1 metre mounted on a wooden board as shown in diagram below. A unknown resistance X is connected on one side of the bridge and a resistance box having known value R is connected on other side of the bridge.A galvanometer along with jockey is mounted between two resistance to form a wheatstone network.

Diagram: 

Working : when the potential difference is applied between two ends of the conductor having length 1 metre, the current is divided at junction according to kirchoff's current law. The jockey of the galvanometer is tapped on the wire in order to adjust both end of the galvanometer at same potential so that the current through galvanometer become zero. Let us consider point L₁ is obtained from left such that at this point galvanometer shows null deflection. The value of length is noted and L₂ is obtained using mathematical calculation. Now bridge is said to be in balanced condition.

According to wheatstone bridge,

X / R = (ρL₁ / A) / (ρL₂ / A) ----------- ( R= (ρL / A)

X / R = L₁ / L₂

X / R = L₁ / (100- L₁) --------------(A)   ( L₂ = 100 - L₁)

Equation no (A) gives value of unknown resistance .

Errors in Experiment: 

1)  If the cross section of the wire is not uniform , it will leads to error in measurement.

2) The end where the wire are joined , a contact resistance is developed.

3) There might be problem in measuring length.

Precautions to reduce errors:

1) The resistance should be so adjusted that null deflection is  obtained between 33cm to 66cm.

2) Take minimum 3 reading and obtain mean.

3) The jockey should be tapped on the wire and it should not be slided on it.

4) try experiment by interchanging the position of unknown resistance and resitance box.

 <<< Wheatstone Bridge│ │ Kelvin's Bridge>>> 

---

Read More

Wheatstone Bridge

                                           Wheatstone Bridge

Wheatstone is a device used for measuring resistance ( 10 ohm to 100 ohm approximately).It was discovered by Charles wheatstone (1807-1875) .

Principle : It works on the principle of null deflection. When the potential between two point is equal no current flow through galvanometer and the bridge is said to be in balanced condition.

Construction : It consist of four resistance connected in a manner to form a Quadrilateral ABCD. as shown in fig below. A potential difference is connected between point A and C such that point A is at highest potential and point C is at lowest potential. A galvanometer is connected between point B and D to form a bridge.

Diagram : 

Solution: When the potential difference is applied between two point A and C , the current I start flowing through the circuit .At point A the current gets divided as  I₁ in branch AB and  I₂ in branch AD. The galvanometer is connected such that the potential at point B and D are at same potential so that no current flow through the galvanometer i.e Ig = 0. (Balanced condition is achieved)

Applying KVL in loop ABDA,

I₁ R₁ + 0  - I₂ R₃ = 0

I₁ R₁ = I₂ R₃

I₁ / I₂ = R₃ / R₁ -----------(A)

Applying KVL in Loop BCDB,

(I₁-Ig)R₂ -(I₂+Ig)R₄ - Ig =0

putting Ig =0 as no current flow through galvanometer

I₁ R₂ = I₂ R₄

I₁ / I₂ = R₄ / R₂ -----------(B)

 From A and B,

 

R₃ / R₁ = R₄ / R₂

adjusting above equation,

R₁ / R₂ = R₃ / R₄ ------------(3)

With the help of equation (3) we can find out unknown resistance if three resistance is known.

                                   <<< KVL & KCL│ │ Metre's Bridge>>> 

---

Read More

Kirchoff 's law

 Kirchoff 's Current law: The algebric sum of all the current at a junction is equal to zero.

 Σ I = 0  

Thus From Above Equation we can state that : The current entering the junction is always equal to current leaving the Junction.

---

Kirchoff's Voltage law: The sum of all the EMF and Potential difference in a closed loop is equal to Zero.

                                                   Σ Emf + Σ IR = 0  

---

Sign Conventions used while applying Kirchoff 's Law : 

1) The potential difference  to be taken negative when we are tracing the loop in direction opposite to direction of flow of current.

2) The EMF to be taken positive when we are tracing from positive terminal to negative terminal of emf.

( Note:  The sign convention can be taken opposite of the condition mentioned above)

 <<< Introduction│ │ Wheatstone Bridge>>>

---

Read More