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 gradu- ally 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.
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 gradu- ally 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.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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Transcribed Image Text: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 gradu-
ally 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.
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