The Heaviside function defined in Exercise 57 can also be usedto define the ramp function y=c t H(t), which represents agradual 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 graduallyincreased to 120 volts over a 60 -second time interval. Writea formula for V(t) in terms of H(t) for t ⩽ 60.(c) Sketch the graph of the volta
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The Heaviside function H is defined by H(t) = { 0 1 . 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 of the voltage V
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