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ACKNOWLEDGMENTS
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I would like to thank Rayjan Wilson for his thorough and thoughtful review of the manuscript His insightful comments and detailed review were vital to making this book a success
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An Introduction to Circuit Analysis
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An electric circuit is an arrangement into a network of several connected electric components The components that we will be concerned with are two-terminal components This means that each component has two connection points or terminals that can be used to connect it with other components in the circuit Each type of component will have its own symbol This is illustrated in Fig 1-1, where we indicate the terminals with two rounded ends or dots and use an empty box to represent a generic electric component There are several electric components but in this book our primary focus will be on resistors, capacitors, inductors, and operational ampli ers At this point, we won t worry about what these components are We will investigate each one in detail later in the book as the necessary theory is developed In this chapter we will lay down a few fundamentals We begin by de ning circuit analysis
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Circuit Analysis Demysti ed
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Terminal Symbol for specific electrical component
Terminal
Fig 1-1 A diagram of a generic two-terminal electric component
What Is Circuit Analysis
The main task of circuit analysis is to analyze the behavior of an electric circuit to see how it responds to a given input The input could be a voltage or a current, or maybe some combination of voltages and currents As you might imagine, electric components can be connected in many different ways When analyzing a circuit, we may need to nd the voltage across some component or the current through another component for the given input Or we may need to nd the voltage across a pair of output terminals connected to the circuit So, in a nutshell, when we do circuit analysis we want to nd out how the unique circuit we are given responds to a particular input The response of the circuit is the output This concept is illustrated in Fig 1-2 To begin our study of circuit analysis, we will need to de ne some basic quantities like current and voltage more precisely
Electric Current
Electric charge is a fundamental property of subatomic particles The amount of electric charge that a particle carries determines how it will interact with
Input to circuit Electrical Circuit
Output or response of circuit
Fig 1-2 The task of circuit analysis is to nd out what the output or response of an electric circuit is to a given input, which may be a voltage or current
An Introduction to Circuit Analysis
electric and magnetic elds In the SI system, which we will use exclusively in this book, the unit of charge is the coulomb The symbol for a coulomb is C An electron carries an electric charge given by charge of single electron = 16 10 19 C (11)
The electric charge in an element or region can vary with time We denote electric charge by q(t), where the t denotes that charge can be a function of time The ow of charge or motion of charged particles is called electric current We denote electric current by the symbol i(t), where the t denotes that current can be a function of time The SI unit for current is the ampere or amp, indicated by the symbol A One amp is equal to the ow of one coulomb per second 1 A = 1 C/s (12)
Current is formally de ned as the rate of change of charge with time That is, it is given by the derivative i(t) = dq (amperes) dt (13)
EXAMPLE 1-1 The charge in a wire is known to be q(t) = 3t 2 6 C Find the current SOLUTION Using (13), we have i(t) = dq d = (3t 2 6) = 6t A dt dt
EXAMPLE 1-2 Find the current that corresponds to each of the following functions of charge: (a) q(t) = 10 cos 170 t mC (b) q(t) = e 2t sin t C (c) q(t) = 4e t + 3e5t C SOLUTION In each case, we apply (13) paying special attention to the units In (a), we have q(t) = 10 cos 170 t mC Since the charge is measured in millicoulombs
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