0195136047.pdf

50 CIRCUIT CONCEPTS

V

Rb Ra

Rs Rx

A

Figure 1.4.2Basic Wheatstone bridge circuit for resistance

measurement.

EXAMPLE 1.4.2

Redraw the Wheatstone bridge circuit of Figure 1.4.2 and show that Equation (1.4.1) holds good

for the null condition when the meterAreads zero current.

Solution

Rb Rs

PQ

Ra

vPQ = 0

Rx

v

Figure E1.4.2Figure 1.4.2 redrawn.

Under null condition,VPQ=0, orPandQare at the same potential. Using the voltage division

principle,

(

V

Rb+Ra

)

Rb=

(

V

Rs+Rx

)

Rs

yieldingRxRb=RaRs, which is the same as Equation (1.4.1).

1.5 Analogy between Electrical and Other Nonelectric Physical Systems

Systems such as those encountered in mechanics, thermodynamics, and hydraulics can be repre-

sented by analogous electric networks, from the response of which the system characteristics can

be investigated. Theanalogy, of course, is a mathematical one: that is, two systems are analogous

to each other if they are described by similar equations. The analogous electric quantities for a

mechanical system are listed in Table 1.5.1.

Consider a tank filled with water, as shown in Figure 1.5.1, with input flow rateFiand output

flow rateFo=h/R, wherehis the fluid level or head andRis related to the diameter of the

pipe, denoting the fluid resistance. LetAbe the cross-sectional area of the tank. We may think of

the fluid as being analogous to charge, and the fluid flow as being analogous to current. Then, in

effect, the water tank acts as a capacitor storing charge, which is fluid in this case. This analogy

is illustrated in Table 1.5.2.