Answer the following. [a] In the textbook\'s Fig. P10.2-1, the current through t

Question

Answer the following. [a] In the textbook's Fig. P10.2-1, the current through the inductor, i_L(t) = (1/L) integral^t_-infinity v_L(tau) d tau, is a state variable, just as the q_1, q_2 and q_3 of Fig.10.5(a) are state variables. However, the voltage across the inductor, v_L(t) = L di_L/dt is not a state variable. Why is i_L(t) a state variable if v_L(t) is not? [b] Is the voltage v_R(t) across a resistor a state variable? Briefly, why or why not? Is the current i_R(t) through a resistor a state variable? [c] Identify the two state variables in the textbook's Fig. P10.2-2.

Explanation / Answer

State variables are memory elements i.e the elements which have the property to store.

(a) Inductor is simply a wire wonded as a coil having a property of obstructing sudden change in current. So in case of inductor when there is this sudden change in current, for some time it retains the previous value only which means it is having some memory where it stores the previous value.

Therefore inductor current is taken as state variable. In the case of voltage (not state variable), its change is completely based on the current i.e., its just acts an outcome rather than a cause.

(b) Resitor is a passive component that obstructs the flow of current but it doesn’t have the property of storing or retaining in previous state. So its not a state variable.

© The state varibales are Vc(t) [ capacitor volatge], Il(t) [ inductor current].

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