The Heaviside function H is defined by It is used in the study of electric circuits to
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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 t.
(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 of 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 correspond to a translation.)
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a c Ht 240 0 1 0 if t 0 1 if t 0 5 b Vt VA 120 0 if t 0 120 ...View the full answer
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