Question

obtain the relation r1/r2=r3/r4 for the wheatstone 's bridge the symbol have their standard meaning​

Answer 1

Explanation:

Wheatstone's bridge: An important application of Kirchoff's law is the Wheatstone's bridge figure.

Wheatstone's network consists of 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 I

g

. The resistance of galvanometer is G.

Applying Kirchoff's current law to junction B,

I

1

−I

g

−I

3

=0 ............(1)

Applying Kirhcoff's current law of junction D.

I

2

+I

g

−I

4

=0 ...............(2)

Applying Kirchoff's voltage law to closed path ABDA

I

1

P+I

g

G−I

2

R=0 ..............(3)

Applying Kirchoff's voltage law to closed path ABCDA

I

1

P+I

3

Q−I

4

S−I

2

R=0 .............(4)

When the galvanometer shows zero deflection, the points B and D are at same potential and I

g

=0. Substituting I

g

=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

I

1

(P+Q)

=

I

2

R

I

2

(R+S)

∴

P

P+Q

=

R

R+S

⇒1+

P

Q

=1+

R

S

∴

P

Q

=

R

S

or

Q

P

=

S

R

.

This is the condition for bridge balance. If P, Q and R are known, the resistance S can be calculated.

solution