Wheatstone bridge, Meter bridge - explanation , Practice problems, FAQs

Nimit has four resistors with him in his physics lab. Three of them have color codings on them; in order to find their resistance, he recalls the digit corresponding to each color. But the fourth resistor has no color bands. Now how is he going to find its resistance? A device called Wheatstone bridge is going to help him find the unknown resistance. Scientist Samuel Hunter Christie invented the wheatstone bridge in 1833, which was later developed by Sir Charles Wheastone in 1843. 

Table of contents:

• What is Wheatstone bridge?
• Principle of wheatstone bridge
• Wheatstone bridge derivation
• Applications of wheatstone bridge
• Limitations of wheatstone bridge 
• Meter bridge 
• Meter bridge derivation
• Practice problems
• FAQs

What is Wheatstone bridge?

Wheatstone bridge, also known as the resistance bridge, consists of four resistors, connected in four places known as “arms” of the circuit. In the following diagram, and are four resistors which are connected as shown. Out of these , the resistor is unknown. The whole arrangement of resistors is connected to a battery of emf A galvanometer of resistance is connected between the points and . 

                    Fig showing the connection of resistors in a Wheatstone bridge

Principle of wheatstone bridge

A wheatstone bridge works on the principle of null-deflection; when the ratio of resistances in the left arm is equal to the ratio of resistances in the right arm, the bridge is said to be in a “balanced condition”. When this is achieved, then the galvanometer shows no deflection. When the bridge is in unbalanced condition, the ratio of the resistances is not equal.

Wheatstone bridge derivation

The current flowing from the battery divides into and at the junction is the current flowing through is the current flowing through and are the currents flowing through Q and S. Let be the current flowing through the galvanometer, and be the galvanometer resistance. Applying Kirchoff’s voltage law in loopabda, we get 

When the bridge is balanced, the galvanometer shows null deflection, i.e

Let be the current flowing in resistor and be the current flowing in resistor

 Applying Kirchoff’s Rule in loop bcdb

when

Applying junction rule at node b,

Applying junction rule at node d,

 
Substituting equations and in equation and we get 

Dividing the above two equations, we get

=

Equation gives the condition for a balanced wheatstone bridge. The value of the unknown resistance can be calculated by cross-multiplication. 

Applications of wheatstone bridge

• It is used to give a precise value of the resistance to be measured.
• Parameters like impedance, inductance, capacitance can be measured.

Limitations of wheatstone bridge

• It is only accurate for measurements of low resistance. If the unknown resistance has a huge value, then the galvanometer becomes difficult to balance.
• When the resistance draws a huge current from the circuit, it displays heating effect ( heat dissipated in a resistor This leads to an inaccurate reading.

Meter Bridge

A meter bridge, also known as a Carey Foster or slide wire bridge, has a working principle similar to that of Wheatstone bridge. A wire having length of is clamped between metallic strips. It has a uniform cross sectional area and low temperature coefficient of resistance. In the space between the strips, the unknown resistor and known resistor are connected. One end of a jockey is pressed on the wire while the other end is connected to a galvanometer. The jockey is moved on the wire till the galvanometer shows null deflection. The corresponding length measured from end is noted as the balancing length of unknown resistance The balancing length corresponding to the known resistance becomes The experiment is repeated and the values of are noted. The average of the readings is taken.

Meter bridge derivation

According to the working principle of meter bridge, the resistance is directly proportional to its corresponding balancing length. Let be the balancing length corresponding to the resistance Then is the length corresponding to the resistance  

Dividing equations and we get 

From the above equation, the value of can be found by cross multiplication.

Practice problems

Q. In a Wheatstone’s bridge, the values of resistances are as follows: If the galvanometer shows zero deflection, determine the value of S.?

(a) (b) (c) (d)

A. a 

Q. In the given figure, find the value of resistance when the Wheatstone’s network is balanced?

(a) (b) (c) (d)

A. d

( denotes the effective resistance of and connected in series).

When a wheatstone bridge is balanced, 

Q. In a meter bridge with a standard resistance of in the right gap, the ratio of balancing length is . Find the value of the other resistance.

A. Given . Let be the unknown resistance. Then,

Q. In a meter bridge, the value of resistance in the resistance box is . The balancing length corresponding to this resistance is . Find the value of unknown resistance.

(a) (b) (c) (d)

A. a

FAQs:

Q. What happens to the balancing length in a meter bridge when the resistances are interchanged?
A. When the resistances are interchanged, the balancing lengths also are interchanged.

Q. Write the equation for resistance of a meter bridge wire, having length and area
A. Resistance

specific resistance.

Q. What is the wheatstone bridge also known as?
A. It is also known as ohmmeter. 

Q. What does an unbalanced wheatstone bridge mean?
A. An unbalanced bridge means the ratio of the resistances in the left arm is not equal to the ratio of the resistances in the right arm.