tailieunhanh - Lecture Electric circuits analysis - Lecture 28: Step response of an RL circuit
In this chapter, the following content will be discussed: Source free RL and RC circuits, unit step function, step response of RC circuit, step response of RL circuit. | Step Response of an RL Circuit Our goal is to find the inductor current i as the circuit response. An RL circuit with a step input voltage. Lecture 28 This is the complete response of the RL circuit Total response of the RL circuit with initial inductor current Io. Thus, to find the step response of an RL circuit requires three things: 1. The initial inductor current i(0) at t = 0+. 2. The final inductor current i(∞). 3. The time constant τ . if the switching takes place at time t = t0 instead of t = 0,then above Eq. becomes Step responses of an RL circuit with no initial inductor current: (a) current response, (b) voltage response Example 3 Find i(t) in the circuit in following Fig. for t > 0. Assume that the switch has been closed for a long time. Example 4 At t = 0, switch 1 in the following circuit is closed, and switch 2 is closed 4 s later. Find i(t) for t > 0. Calculate i for t = 2 s and t = 5 s. | Step Response of an RL Circuit Our goal is to find the inductor current i as the circuit response. An RL circuit with a step input voltage. Lecture 28 This is the complete response of the RL circuit Total response of the RL circuit with initial inductor current Io. Thus, to find the step response of an RL circuit requires three things: 1. The initial inductor current i(0) at t = 0+. 2. The final inductor current i(∞). 3. The time constant τ . if the switching takes place at time t = t0 instead of t = 0,then above Eq. becomes Step responses of an RL circuit with no initial inductor current: (a) current response, (b) voltage response Example 3 Find i(t) in the circuit in following Fig. for t > 0. Assume that the switch has been closed for a long time. Example 4 At t = 0, switch 1 in the following circuit is closed, and switch 2 is closed 4 s later. Find i(t) for t > 0. Calculate i for t = 2 s and t = 5 . | Step Response of an RL Circuit Our goal is to find the inductor current i as the circuit response. An RL circuit with a step input voltage. Lecture 28 This is the complete response of the RL circuit Total response of the RL circuit with initial inductor current Io. Thus, to find the step response of an RL circuit requires three things: 1. The initial inductor current i(0) at t = 0+. 2. The final inductor current i(∞). 3. The time constant τ . if the switching takes place at time t = t0 instead of t = 0,then above Eq. becomes Step responses of an RL circuit with no initial inductor current: (a) current response, (b) voltage response Example 3 Find i(t) in the circuit in following Fig. for t > 0. Assume that the switch has been closed for a long time. Example 4 At t = 0, switch 1 in the following circuit is closed, and switch 2 is closed 4 s later. Find i(t) for t > 0. Calculate i for t = 2 s and t = 5 . | Step Response of an RL Circuit Our goal is to find the inductor current i as the circuit response. An RL circuit with a step input voltage. Lecture 28 This is the complete response of the RL circuit Total response of the RL circuit with initial inductor current Io. Thus, to find the step response of an RL circuit requires three things: 1. The initial inductor current i(0) at t = 0+. 2. The final inductor current i(∞). 3. The time constant τ . if the switching takes place at time t = t0 instead of t = 0,then above Eq. becomes Step responses of an RL circuit with no initial inductor current: (a) current response, (b) voltage response Example 3 Find i(t) in the circuit in following Fig. for t > 0. Assume that the switch has been closed for a long time. Example 4 At t = 0, switch 1 in the following circuit is closed, and switch 2 is closed 4 s later. Find i(t) for t > 0. Calculate i for t = 2 s and t = 5 s.
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