Single Variable Calculus, Chapter 1, 1.3, Section 1.3, Problem 57

The Heaviside function $H$ is defined by $H(t)$ = $\left\{\begin{array}{cccc}
0 & if & t < 0 \\
1 & if & t\geq 0
\end{array} \right.$


Suppose that it is used in the study of electric circuits to represents the sudden surge of electric current, or voltage, when a switch is instantaneously turned on.

Sketch the graph of the Heaviside function.








Find a formula for $V(t)$ in terms of $H(t)$ and sketch a 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.









V(t) = 120 H(t)

Find a formula for $V(t)$ in terms of $H(t)$ and sketch a graph of the voltage $V(t)$ in a circuit if the switch is turned on at time $t = 5$ and 240 volts are applied instantaneously to the circuit. (Note that starting at $t = 5$ corresponds to a translation.)









V(t) = 240 H(t-5)