Question: 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

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 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.)

if o ift<0 H(t) |1 if t 0

if o ift

Step by Step Solution

★★★★★

3.46 Rating (172 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

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 full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

M-C-F-M (77).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

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)...

If H is the Heaviside function defined in Example 6 in Section 2.2, prove, using Definition 2, that lim t H(t) does not exist.

The switch in figure is closed at t = 0. Sketch the voltage and current at the right side of the switch for 0 t= 0 22, Zo. Y 27 V 0.5 Zo z = L z = 0

The Heaviside function H is defined by H (t ) = 10 if t The Heaviside function H is defined by O if t

The sensitivity of a relay refers to the smallest value of the actuating quantity at which the relay operates detecting any abnormal condition. In case of an over current relay, mathematically this...

In case of an over current relay, mathematically this can be defined as the ratio between the short circuit fault current (Is) and The relay operating current (Io). The value of Io should not be too...

The relay operating current (Io). The value of Io should not be too small or large so that the relay is either too sensitive or slow in responding. Damage to the equipment due to abnormally large and...

Damage to the equipment due to abnormally large and unbalanced currents and low voltages produced by the short circuits Explosions may occur in the equipments which have insulating oil, particularly...

With a particular number of towers the chances of incidence of lightning on power conductor scan be minimized by placing a ground wire at the top of the tower structure.. The tower presents a...

The value of Io should not be too small or large so that the relay is either too sensitive or slow in responding. Damage to the equipment due to abnormally large and unbalanced currents and low...

Detection of rigged school milk prices (contd). Refer to the investigation of collusive bidding in the northern Kentucky school milk market, presented in Exercise. Market allocation is a common form...

Sandpaper is rated by the coarseness of the grit on the paper. Sandpaper that is more coarse will remove material faster. Jobs such as the final sanding of bare wood prior to painting or sanding in...

John Hill owns 5 1 % of the capital stock of Hill Corporation, Which of the following actions would not be permissble for John Hill to take? A To cause those persons he chooses to become drectors of...

Prepare a cost of goods sold budget for the Summit Manufacturing Company for the year ended December 31, 2011, from the following estimates. Inventories of production units: : Direct materials...

Cash Flow Hedge on January 2, 2010, Parton Company issues a 5-year, $10,000,000 note at LIBOR, with interest paid annually. The variable rate is reset at the end of each year. The LIBOR rate for the...

A rock is thrown vertically upward from ground level at time t = 0. At t = 1.5 s it passes the top of a tall tower, and 1.0 s later it reaches its maximum height. What is the height of the tower?

Petty Cash The petty cash fund of Teasdale's Auto Repair Service, a sole proprietorship, contains the following. The general ledger account Petty Cash has a balance of $300. Prepare the journal entry...

Account analysis method. Lorenzo operates a car wash. Incoming cars are put on an automatic conveyor belt. Cars are washed as the conveyor belt carries them from the start station to the finish...

Consider the isomerization of butane with an equilibrium constant of K = 2.5. (See Study Question 13.) The system is originally at equilibrium with [butane] = 1.0 M and [isobutane] = 2.5 M. (a) If...

(a) Find the slope of the tangent to the curve y = 3 + 4x2 - 2x3 at the point where x = a. (b) Find equations of the tangent lines at the points (1, 5) and (2, 3). (c) Graph the curve and both...

Use the given graph to estimate the value of each derivative. Then sketch the graph of f'. (a) f'(- 3) (b) f'(-2) (c) f'(- 1) (d) f'(0) (e) f'(1) (f) f'(2) (g) f'(3) 1

A rechargeable battery is plugged into a charger. The graph shows C(t), the percentage of full capacity that the battery reaches as a function of time elapsed (in hours). (a) What is the meaning of...

Peaceful Cruises wants to build a new cruise ship that has an initial investment of $ 4 5 0 million. It is estimated to provide an annual cash flow over the next 2 0 years of $ 5 8 million per year....

Suppose that an investor has 8 years investment horizon. The investor is considering a 15-year semi-annual coupon bond selling at par and having a coupon rate of 9%. The investor expectations are as...

0 1 You are paying an apartment for lease at $400 per month for 25 months, monthly interest rate is 12.8%. The first payment is made today. What is the value of your 25 months apartment lease today?...