   Chapter 1.3, Problem 60E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# The Heaviside function defined in Exercise 59 can also be used to define the ramp function y = ctH(t), which represents a gradual increase in voltage or current in a circuit.(a) Sketch the graph of the ramp function y = tH(t).(b) Sketch the graph of the voltage V(t) in a circuit if the switch is turned on at time t = 0 and the voltage is gradually increased to 120 volts over a 60-second time interval. Write a formula for V(t) in terms of H(t) for t ≤ 60.(c) Sketch the graph of the voltage V(t) in a circuit if the switch is turned on at time t = 7 seconds and the voltage is gradually increased to 100 volts over a period of 25 seconds.  Write a formula for V(t) in terms of H(t) for t ≤ 32.

(a)

To determine

To sketch: The graph of the ramp function y=tH(t) .

Explanation

Heaviside function is, H(t)={0      if t<01if t0 .

So, the ramp function is, R(t)=tH(t)

(b)

To determine

To sketch: The graph of circuit if the switch is turned at t = 0 and the voltage gradually increased to 120 volts in 60 seconds; write the formula for V(t) in terms of H(t) for

t60 .

(c)

To determine

To sketch: The graph of the voltage in a circuit if the switch is turned at t = 7 seconds and gradually increased t0 100 volts over a period of 25 seconds; write the formula for V(t) in terms of H(t) for t32 .

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