Question

What is Wheatstone bridge? Deduce the balanced condition of it with the help of Kirchhoff’s law.

Answer 1

Construction : The construction of Wheatstone’s bridge is shown in following diagram (figure) in which a quadrilateral ABCD is prepared by

connecting four resistances P, Q, R and S. A cell is connected between the points A and C through key K₁ which is known as battery key and a galvanometer between the point B and D through another key K₂ which is known as galvanometer key. If on pressing the key K₁ and K₂, there is no deflection in galvanometer, then the bridge is said to be balanced condition. In this situation the relation between all the resistances is given by:

\(\frac{P}{Q}=\frac{R}{S}\)

Principle of Wheatstone Bridge and Condition of Balance:

When battery key K₁ is pressed, then main current I starts flowing in the circuit. At junction A this current splits in two parts I₁ and I₂ as shown in figure. These currents I₂ and I₂ again obtain two paths at junctions B and D respectively. Now following three situations are possible:

(i) When V_B > V_D. then current I₂ passes as such through resistance S but current I₁ splits in two parts at junction B, one part I_g passes through galvanometer showing deflection in one direction while rest current (I₁ – I_g) passes through Q.

(ii) When V_B < V_D. then opposite situation to previous situation (i) is observed i.e. .current I₂ splits in two parts at D. Now the current I_g produces deflection in galvanometer in opposite direction to previous deflection.

(iii) When V_B = V_D, then no current passes through galvanometer i.e. galvanometer shows no deflection because now I _g = 0. This situation is said to be balance condition of Wheatstone bridge. It is clear that current is flowing in the circuit but there is no effect of current on galvanometer arm which resembles with the bridge on a river. This is why this circuit is called ‘Bridge circuit’ Thus in balanced condition.

Therefore, “it is clear that in balanced situation of the bridge, the ratio of resistances of any two corresponding arms of quadrilateral ABCD is equal to ratio of two remaining corresponding arms”.
From equation (3).
S = \(\frac{Q}{P} \times R\)
Thus, by determining the balanced situation, unknown resistance can be determined.
The arms of Wheatstone bridge are known as particulars names given below:
(i) P and Q are called ratio arms.
(ii) R is called variable resistance arm.
(iii) S is called unknown resistance arm.