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Ground The choice of the word ground is not arbitrary This point can be illustrated by a simple analogy with the physics of uid motion Consider a tank of water, as shown in Figure 251, located at a certain height above the ground The potential energy due to gravity will cause water to ow out of the pipe at a certain ow rate The pressure that forces water out of the pipe is directly related to the head, (h1 h2 ), in such a way that this pressure is zero when h2 = h1 Now the point h3 , corresponding to the ground level, is de ned as having zero potential energy It should be apparent that the pressure acting on the uid in the pipe is really caused by the difference in potential energy, (h1 h3 ) (h2 h3 ) It can be seen, then, that it is not necessary to assign a precise energy level to the height h3 ; in fact, it would be extremely cumbersome to do so, since the equations describing the ow of water would then be different, say, in Denver (h3 = 1,600 m above sea level) from those that would apply in Miami (h3 = 0 m above sea level) You see, then, that it is the relative difference in potential energy that matters in the water tank problem
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h2 Flow of water from pipe h3 Physical ground
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Figure 251 Analogy between electrical and earth ground
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In analogous fashion, in every circuit a point can be de ned that is recognized as ground and is assigned the electric potential of zero volts for convenience Note that, unless they are purposely connected together, the grounds in two completely separate circuits are not necessarily at the same potential This last statement may seem puzzling, but Example 212 should clarify the idea It is a useful exercise at this point to put the concepts illustrated in this chapter into practice by identifying the relevant variables in a few examples of electrical circuits In the following example, we shall illustrate how it is possible to de ne unknown voltages and currents in a circuit in terms of the source voltages and currents and of the resistances in the circuit
EXAMPLE 212
Identify the branch and node voltages and the loop and mesh currents in the circuit of Figure 252
2
Fundamentals of Electric Circuits
+ vR1 _ R1 R2
+ vR3 _ R3 + + vR4 vR2 i _ b _ d
Solution
The following node voltages may be identi ed:
Node voltages va vb vc vd = vS (source voltage) = vR2 = vR4 = 0 (ground) Branch voltages vS = va vd = va vR1 = va vb vR2 = vb vd = vb vR3 = vb vc vR4 = vc vd = vc
+ vS _ ia _
Comments: Currents ia , ib , and ic are loop currents, but only ia and ib are mesh currents
It should be clear at this stage that some method is needed to organize the wealth of information that can be generated simply by applying Ohm s law at each branch in a circuit What would be desirable at this point is a means of reducing the number of equations needed to solve a circuit to the minimum necessary, that is, a method for obtaining N equations in N unknowns The next chapter is devoted to the development of systematic circuit analysis methods that will greatly simplify the solution of electrical network problems