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Current Electricity — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsCurrent Electricity5 Marks
Question
What is Wheatstone bridge ? Explain its use in detail.
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Answer

Wheatstone Bridge: It is an arrangement of four resistance used to measure one of them in terms of the other three resistances. It was devised by a scientist of England Professor C.F. Wheatstone in 1843 and in his honour it is known as Wheatstone bridge. It is one of the most accurate methods for measuring resistance.
Construction: Wheatstone bridge consists of four resistances P, Q, R and S connected in series so as to form a closed loop in the form of a quadrilateral ABCD. A cell E is connected between diagonally opposite corners of one of its diagonals (say between A and C) through a key $K_1$. A galvanometer G is connected between diagonally opposite corners of the other diagonal (say between B and D) through a key $K_2$. The whole ar-rangement is shown in adjoining figure.
Image
Principle : If the resistances forming the four arms of the quadrilateral are so adjusted that on sending current in the closed loop by the cell, there is no deflection in the galvanometer then Wheatstone Bridge is said to be balanced. In this condition the ratio of the resistances in any of the two adjacent arms of the quadrilateral is equal to the ratio of the resistances in the remaining two adjacent arms.
In this way for Wheatstone Bridge shown in adjoin-ing fig. in its balanced position, we have
$ \frac{P}{Q} = \frac{R}{S} $
This relation is known as balanced condition of Wheatstone bridge.
Proof : When key $K_1$ is pressed current I drawn from the cell E is divided into two parts at A. One part $I_1$ flows in the arm AB and the other part $I_2$ in the arm AD of the quadrilateral.
In the beginning, on pressing $K_2$; the galvanometer G shows deflection. This means that the current in the arm BD flows either from B to D or from D to B according to the situation B is at higher potential than D or vice-versa. Now the values of resistance P, Q, R and S, are so adjusted that there is no deflection in the galva-nometer. In this condition bridge is said to be balanced. This condition is obtained only when potentials at B and D are equal. Consequently, the current flowing in AB and BC arms is I, and in arms AD and DC it is 12. These currents recombine at C to form again current I. Thus circuit of cell is completed. In the balanced position of Wheatstone Bridge there is no current in the diagonal BD through galvanometer G. On applying Kirchhoff's second law for closed loop ABDA, we have
$
I_1 P-I_2 R=0 \Rightarrow I_1 P=I_2 R
$ ...(1)
In the same way for closed loop BCDB, we have
$I_1 Q-I_2 S=0 \Rightarrow I_1 Q=I_2 S$ ...(2)
Dividing eq. (1) by eq. (2), we get
$\frac{P}{Q}=\frac{R}{S}$ ...(3)
Resistance R and ratio P/Q are known, hence un-known resistance S can be determined by equation (3). This is the balanced condition of the bridge. For this rea-son, the P and Q arms are known as ratio arms, arm R as known arm and arm S as unknown arm. In the balanced position of the bridge on interchanging the positions of the cell and galvanometer, balanced position of the bridge remains unchanged. Therefore, the arms BD and CD are called conjugate arms of the bridge.
Determination of specific resistance of the ma-terial of a given wire : Meter Bridge and Post Office Box are two apparatus based on the principle of Wheat-stone bridge. With the help of one of these apparatus using formula (3) the unknown resistance of the given wire S is calculated and using the following formula specific resistance 'ρ' of the material of the given wire may be calculated :
$\rho=\frac{\pi r^2 S}{l} \quad\left\{\because R =\rho \frac{1}{A}=\rho \times \frac{1}{\pi r^2}\right\}$
where r = radius of the wire, which is measured by screw gauge.
l = length of the wire which is measured by metre scale.
On the basis of principle of Wheatstone Bridge, meter bridge and post office box two instruments are divided to calculate unknown resistance.

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