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Resistance and SelfInductance
Figure 17 shows a schematic diagram of an RL circuit. When there is current in such a circuit, the selfinductance has energy that is stored electromagnetically. The electrical energy in the resistance is converted into thermal energy. The mathematical relationships in this kind of circuit are very similar to those in the mechanical system involving mass and friction.
In Fig. 17 the applied voltage V is constant and equals two components
e_{R} = i_{R}, the resistance drop Equation 137 can be rewritten as
and the power is expressed by
The electric power converted into heat is Ri^{2} and that stored electromagnetically is Li di/dt. The energy relationship is expressed by the following
If the initial conditions are i = 0 when t = 0, then Eq. 138 becomes
where Li^{2}/2 represents the energy stored in the selfinductance. If the initial conditions are such that i = 0 when t = 0, the current in the RL circuit is expressed by
The reciprocal L/R of the constant term in the exponent of Eq. 140 is the time constant t. It corresponds to the time constant M/R_{F} in the mechanical system.
A comparison of Eq. 134 with 140 shows that if voltage is taken as analogous to force and electrical resistance as analogous to frictional resistance in the mechanical system, current corresponds to velocity and selfinductance to inertia. Curves similar to those shown in Fig. 18 would portray the relationships for the mechanical system. Thus the curve of current i vs time could be used to relate the velocity v to time in the mechanical system. Similarly, the curve of p_{φ} vs time could be used to represent the mechanical power Mv dv/dt, which stores energy in the moving mass of the mechanical system. The energy 1/2Mv^{2} stored in the mass could also be represented as a function of time by the curve of W_{L} vs time.


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