Alexander-Sadiku
Fundamentals of Electric Circuits

	Chapter 7
	First-Order Circuits

First-Order Circuits
Chapter 7

	7.1 The Source-Free RC Circuit
	7.2 The Source-Free RL Circuit
	7.3 Unit-step Function
	7.4  Step Response of an RC Circuit
	7.5 Step Response of an RL Circuit

7.1 The Source-Free
RC Circuit (1)

	A first-order circuit is characterized by a first-order differential equation.

7.1 The Source-Free
RC Circuit (2)

	The natural response of a circuit refers to the behavior (in terms of voltages and currents) of the circuit itself, with no external sources of excitation.

7.1 The Source-Free
RC Circuit (3)

	The key to working with a source-free RC circuit is finding:

7.1 The Source-Free
RC Circuit (4)

	Example 1
	Refer to the circuit below, determine vC, vx, and io for t ≥ 0.
	Assume that vC(0) = 30 V.

7.1 The Source-Free
RC Circuit (5)

	Example 2
	The switch in circuit below is opened at t = 0, find v(t) for t ≥ 0.

7.2 The Source-Free
RL Circuit (1)

	A first-order RL circuit consists of a inductor L (or its equivalent) and a resistor (or its equivalent)

7.2 The Source-Free
RL Circuit (2)

7.2 The Source-Free
RL Circuit (3)

7.2 The Source-Free
RL Circuit (4)

	The key to working with a source-free    RL circuit is finding:

7.2 The Source-Free
RL Circuit (5)

	Example 3
	Find i and vx in the circuit.
	Assume that i(0) = 5  A.

7.2 The Source-Free
RL Circuit (6)

	Example 4
	For the circuit, find i(t) for t > 0.

7.3 Unit-Step Function (1)

	The unit step function u(t) is 0 for negative values of t and 1 for positive values of t.

7.3 Unit-Step Function (2)

		voltage source.
		for current source:

7.4 The Step-Response
of a RC Circuit (1)

	The step response of a circuit is its behavior when the excitation is the step function, which may be a voltage    or a current source.

7.4 The Step-Response
of a RC Circuit (2)

	Integrating both sides and considering the initial conditions, the solution of the equation is:

7.4 The Step-Response
of a RC Circuit (3)

	Three steps to find out the step response of an RC circuit:

7.4 The Step-Response
of a RC Circuit (4)

	Example 5
	Find v(t) for t > 0 in the circuit in below. Assume the switch has been open for a long time and is closed at t = 0.
	Calculate v(t) at t = 0.5.

7.5 The Step-response
of a RL Circuit (1)

	The step response of a circuit is its behavior when the excitation is the step function, which may be a voltage or a current source.

7.5 The Step-Response
of a RL Circuit (2)

	Three steps to find out the step response of an RL circuit:

7.5 The Step-Response
of a RL Circuit (4)

	Example 6
	The switch in the circuit shown below has been closed for a long time. It opens at t = 0.
	Find i(t) for t > 0.