The Heaviside function H is defined by H ( t ) = { 0 if t < 0 1 if t ≥ 0 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(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.)
The Heaviside function H is defined by H ( t ) = { 0 if t < 0 1 if t ≥ 0 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(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.)
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(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.)
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