Chapter 1.3, Problem 59E

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8th Edition

James Stewart

ISBN: 9781305270343

Textbook Problem

The **Heaviside function** *H* is defined by

It is used in the study of electric circuits to represent the sudden surge of electric current, or voltage, when a switch is instantaneously turned on.

(a) Sketch the graph of the Heaviside function.

(b) Sketch the graph of the voltage *V*(*t*) in a circuit if the switch is turned on at time *t* = 0 and 120 volts are applied instantaneously to the circuit. Write a formula for *V*(*t*) in terms of *H*(*t*).

(c) Sketch the graph or the voltage *V*(*t*) in a circuit if the switch is turned on at time *t* = 5 seconds and 240 volts are applied instantaneously to the circuit. Write a formula for *V*(*t*) in terms of *H*(*t*)*.* (Note that starting at *t* = 5 corresponds to a translation.)

(a)

To determine

**To sketch:** The graph of the Heaviside function.

Explanation

The Heaviside function is,

(b)

To determine

**To sketch:** The graph of

(c)

To determine

**To sketch:** The graph of the voltage in a circuit if the switch is turned on at t = 5 seconds and 240 volts are applied to the circuit; write the formula for

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