Module 6: Assignment Problems (ELT-490)

| January 11, 2016

 

Module 6: Assignment Problems (ELT-490)

 

 

 

 

 

 

The following 10 exercises build upon your previous education and training along with the sample math problems you studied in this module. The assignment problems will challenge you to put all those elements together.

 

 

 

 

 

Instructions

 

 

 

 

 Attempt all 10 exercises.

 

 

 

 

 

 

 Make sure you answer all parts of each question.

 

 

 

 These exercises are “open reference.” You may use textbook(s), the Internet, and the example materials you studied in this module.

 

 

 

 Do your own work. While you may use other referenced resources, this module is an assessment of your knowledge and ability.

 

 

 

 Show all your work. Do not leave your mentor wondering how you got from one step to the next.

 

 

 

 Submit your solutions electronically using scanned images, preferably pdfs, of your work.

 

 

 

 

 

1 farad

 

 

 

1 henry

 

 

 

2t2 volts

 

 

 

 

 

Exercise 1

 

 

 

Given the following conditions for a simple electrical circuit, as shown in the diagram below, the capacitance is 1 farad, the inductance is 1 henry and the impressed voltage is V volts at time t.

 

 

 

 

The total charge (coulombs) in the circuit at time t is given by the equation ( ) ( )

 

 

 

 

 

 

Determine the formula for the current, and the current at times t = 0 and t = 1. Remember to use radian measures for the trigonometric functions.

 

 

 

Exercise 2

 

 

 

 

The total charge (coulombs) in a given circuit at time t is given by the equation ( ) ( )

 

 

 

 

 

 

Determine the formula for the current, and the current at times t = 0 and t = 2.

 

 

 

Exercise 3

 

 

 

 

In the third assignment, the total charge (coulombs) in the circuit at time t is given by the equation ( ) ( )

 

 

 

 

 

 

Determine the formula for the current, and the current at time t = 2.

 

 

 

Exercise 4

 

 

 

 

In a more complex electrical circuit, the charge is given by the following equation. ( ) ( ) ( )

 

 

 

 

 

 

Determine the equation for the current at any time t, and calculate the current at t=1.

 

 

 

Exercise 5

 

 

 

 

In an electrical circuit, the charge is given by the following equation. ( ) ( )( )

 

 

 

 

 

 

Determine the formula for the current in the circuit at any time t.

 

 

 

Exercise 6

 

 

 

The resistance of a certain component decreases as the current through it increases. The relationship is described by the equation:

 

 

 

 

( ) (ohms)

 

 

 

 

 

 

Determine (a) the current that results in the maximum power in the unit and

 

 

 

(b) the maximum power (watts) delivered to the unit.

 

 

 

 

 

C

 

 

 

S

 

 

 

 

 

 

 

 

 

 

R

 

 

 

 

Exercise 7

 

 

 

 

 

 

Consider the circuit diagram below:

 

 

 

Given conditions:

 

 

 

 

 ℰ= 400 Volts

 

 R = 4000 Ω

 

 C = 5 μ

 

 

 

 

 

 

 τRC

 

 

 

 The charge, q, on the capacitor will increase per the following formula,

 

 

 

 

ℰ ( ))

 

 The current in the circuit is defined by the following formula,

 

ℰ( )

 

 

 

 

 

 

How long does it take for the capacitor to become 97% charged?

 

 

 

 

 

L

 

 

 

S

 

 

 

 

 

 

 

 

 

 

R

 

 

 

 

 

I

 

 

 

Exercise 8

 

 

 

Consider the circuit diagram below, where L is the inductance in henries, I is the current in amperes, and R is the resistance in ohms.

 

 

 

Given conditions:

 

 

 

 

 The formula for current is ℰ( )

 

 Assume the current I was 0 at t =0.

 

 ℰ= 125 Volts

 

 

 

 

 

 

 R = 100 Ω

 

 

 

 L = 25 henries

 

 

 

Calculate the time when the current reaches 400 mA.

 

 

 

 

Exercise 9

 

 

 

 

 

 

Forklifts in a certain plant use electric motors powered by batteries in order to reduce potential hazards from liquid fuels. The general equation for calculating the power available from the battery is given by the equation:

 

 

 

 

P = E I – r I2

 

 

 

 

 

 

Where P = net power (watts) available from the battery

 

 

 

E = the battery potential (volts) with no load

 

 

 

I = the battery current (amps) from the battery

 

 

 

r = the internal resistance (ohms) of the battery

 

 

 

Given Conditions:

 

 

 

E = 80 Volts

 

 

 

 

IMax = 30 amps

 

Calculate the maximum power (Pmax) for the forklift.

 

Exercise 10

 

Given that the charge at a specific location in an electrical circuit is given by the equation( )

 

 

 

 

 

 

What mathematical expression describes the steady-state value of the charge Q(t) as t ?

 

 

 

 

 

Attachments: Module 6: Assignment Problems (ELT-490) The following 10 exercises build upon your previous education and training along with the sample math problems you studied in this module. The assignment problems will challenge you to put all those elements together. Instructions  Attempt all 10 exercises.  Make sure you answer all parts of each question.  These exercises are “open reference.” You may use textbook(s), the Internet, and the example materials you studied in this module.  Do your own work. While you may use other referenced resources, this module is an assessment of your knowledge and ability.  Show all your work. Do not leave your mentor wondering how you got from one step to the next.  Submit your solutions electronically using scanned images, preferably pdfs, of your work. Exercise 1 Given the following conditions for a simple electrical circuit, as shown in the diagram below, the capacitance is 1 farad, the inductance is 1 henry and the impressed voltage is V volts at time t. The total charge (coulombs) in the circuit at time t is given by the equation ( ) ( ) Determine the formula for the current, and the current at times t = 0 and t = 1. Remember to use radian measures for the trigonometric functions. Exercise 2 The total charge (coulombs) in a given circuit at time t is given by the equation ( ) ( ) Determine the formula for the current, and the current at times t = 0 and t = 2. Exercise 3 In the third assignment, the total charge (coulombs) in the circuit at time t is given by the equation ( ) ( ) Determine the formula for the current, and the current at time t = 2. 1 farad 1 henry 2t2 volts Exercise 4 In a more complex electrical circuit, the charge is given by the following equation. ( ) ( ) ( ) Determine the equation for the current at any time t, and calculate the current at t=1. Exercise 5 In an electrical circuit, the charge is given by the following equation. ( ) ( ) ( ) Determine the formula for the current in the circuit at any time t. Exercise 6 The resistance of a certain component decreases as the current through it increases. The relationship is described by the equation: ( ) (ohms) Determine (a) the current that results in the maximum power in the unit and (b) the maximum power (watts) delivered to the unit. Exercise 7 Consider the circuit diagram below: Given conditions:  ℰ = 400 Volts  R = 4000 Ω  C = 5 μF  τ=RC  The charge, q, on the capacitor will increase per the following formula, ℰ( ( ) )  The current in the circuit is defined by the following formula, ℰ ( ) How long does it take for the capacitor to become 97% charged? C S ℰ R Exercise 8 Consider the circuit diagram below, where L is the inductance in henries, I is the current in amperes, and R is the resistance in ohms. Given conditions:  The formula for current is ℰ ( )  Assume the current I was 0 at t =0.  ℰ = 125 Volts  R = 100 Ω  L = 25 henries Calculate the time when the current reaches 400 mA. L S ℰ R I Exercise 9 Forklifts in a certain plant use electric motors powered by batteries in order to reduce potential hazards from liquid fuels. The general equation for calculating the power available from the battery is given by the equation: P = E I – r I2 Where P = net power (watts) available from the battery E = the battery potential (volts) with no load I = the battery current (amps) from the battery r = the internal resistance (ohms) of the battery Given Conditions: E = 80 Volts IMax = 30 amps Calculate the maximum power (Pmax) for the forklift. Exercise 10 Given that the charge at a specific location in an electrical circuit is given by the equation ( ) What mathematical expression describes the steady-state value of the charge Q(t) as t ?

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