One way of stating Kirchhoff's Voltage Law would be to say that the sum of the volt drops in a series circuit must equal the applied voltage.

A) True B) False

The Heaviside function H is defined by

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 theswitch 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 = 5correspondsto a translation.)

The Heaviside function defined in Exercise 59 can also be used to define the ramp function , which represents a gradual increase in voltage or current in a circuit.

(a) Sketch the graph of the ramp function ..

(b) Sketch the graph of the voltage in a circuit if the switch is turned on at time and the voltage is gradually increased to 120 volts over a 60-second time interval.

Write a formula for V(t) in terms of H(t) for

(c) Sketch the graph of the voltage in a circuit if the switch is turned on at time seconds and the voltage is gradually increased to 100 volts over a period of 25 seconds.

Write a formula for in terms of for .

What is the derivative of voltage with respect to time?