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Systems such as those encountered in mechanics, thermodynamics, and hydraulics can be represented by analogous electric networks, from the response of which the system characteristics can be investigated. The analogy, 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.
Consider a tank filled with water, as shown in Figure, with input flow rate Fi and output flow rate Fo = h/R, where h is the fluid level or head and R is related to the diameter of the pipe, denoting the fluid resistance. Let A be 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.
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Q. For a part of the network shown in Figure, given that i 1 = 4A; i 3 (t) = 5e -t , and i 4 (t) = 10 cos 2t, find v 1 , v 2 , v 3 , v 4 , i 2 , and i 5 .
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