Consider an RL electric circuit consisting of a resistor with resistance R (ohms) and an inductor...

 

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Consider an RL electric circuit consisting of a resistor with resistance R (ohms) and an inductor with inductance L (henries) connected in series with an impressed voltage (electromotive force) E(t) (volts). The differential equation governing the current, I (amperes), in this circuit is derived using Kirchoff's Laws and is Suppose that R in seconds. QP L dI dt + RI = E(t) 100 ohms, L = 2.5 henries and the constant impressed voltage is E(t) = Eo = 110 volts. Time, t, is measured (a) If the initial current in the circuit is zero amperes, find the current at any time t, that is, solve the initial value problem. (b) It is often useful to separate solutions of differential equations into transient solutions (those that go to zero as time (t) goes to infinity) and steady state solutions (those that are bounded [constant or periodic] as time goes to infinity, that is, remain after a "long" time). These can be determined by finding the limit as t→∞ of the solution. Find the transient and steady state currents in the circuit. che d (c) Find the time required for the current reach 0.6 ampere. Consider an RL electric circuit consisting of a resistor with resistance R (ohms) and an inductor with inductance L (henries) connected in series with an impressed voltage (electromotive force) E(t) (volts). The differential equation governing the current, I (amperes), in this circuit is derived using Kirchoff's Laws and is Suppose that R in seconds. QP L dI dt + RI = E(t) 100 ohms, L = 2.5 henries and the constant impressed voltage is E(t) = Eo = 110 volts. Time, t, is measured (a) If the initial current in the circuit is zero amperes, find the current at any time t, that is, solve the initial value problem. (b) It is often useful to separate solutions of differential equations into transient solutions (those that go to zero as time (t) goes to infinity) and steady state solutions (those that are bounded [constant or periodic] as time goes to infinity, that is, remain after a "long" time). These can be determined by finding the limit as t→∞ of the solution. Find the transient and steady state currents in the circuit. che d (c) Find the time required for the current reach 0.6 ampere.