Derive a rule to estimate the network resistance when one

Question

Learning Outcome 1

a. Thomas Lord carried out a practical experiment to investigate Ohm's law as part of his engineering science assignment. The results of the investigation are shown in the table below.

V (Volt)	I (Ampere)
23.94324	0.798108
24.00423	0.800141
23.00425	0.766808
24.60483	0.820161
24.80422	0.826807
24.10473	0.803491
23.82423	0.794141
23.90474	0.796825
23.80423	0.793474
23.78914	0.792971
25.00525	0.833508
24.55271	0.818424
24.43898	0.814633
24.45216	0.815072
23.5	0.783333
24	0.8
24.64398	0.821466
23.49992	0.783331
24.34578	0.811526

i). Calculate R and P where R = V/I and P = IV for each set of results using MS Excel(For part ii) and iii) use the first 4 results from the table above.)

ii.) Recalculate R and P to 4, 2, and 1 significant figures respectively by hand

iii). Recalculate R and P to 4, 2, and 1 decimal place respectively by hand

iv). Plot the results of ii) and iii) using all the data using MS Excel.

v). Evaluate the results of the experiment based on your graphs.

b. When three resistors R1, R2 and R3 are connected in parallel as shown in the diagram.

For these resistors the equivalent resistance is given by:

1/R = 1/R₁ + 1/R₂ + 1/R₃

i) Derive a rule to estimate the network resistance when one of the resistors has a much smaller resistance than the other two. (You can use example values to support your answer)

ii) Derive a rule to estimate the network resistance when two of the resistors have much smaller values. (You can use example values to support your answer)

Learning Outcome 2

Convert number systems from one base to another, and apply the binary number system to logic circuits

2)

a. Convert the following decimal numbers to binary:
i) 53₁₀
ii) 0.69875₁₀
iii) 23.90625₁₀

b. Convert the following decimal numbers to binary, via octal:
i) 1465₁₀
ii) 519.4375₁₀

c. Convert the following hexadecimal numbers to binary:
i) ED3₁₆
ii) F3B4₁₆

d. Convert the following binary numbers to decimal numbers:
i) 1 1 1 0 0 0 1 1 0 1 1 0 1 0
ii) 1 0 0 1 1 0 1 1 1 0 0 1 1 1

e. Convert the following hexadecimal numbers to octal numbers:
i) 3BF4₁₆
ii) B5E73₁₆

f. Draw the logic circuit for the Boolean expression

(p.q+ (r  ¯ ). (q + r) + q ¯.(p ¯+q)

g. Find a Boolean function for the logic circuit in the diagram.

Learning Outcome 3

Perform arithmetic operations using complex numbers in Cartesian and polar form

3)

a. Solve the following equation in rectangular form.

7x² + 4x - 8 = 0

b. Given the following complex number

Z₁ = 4∠120⁰
Z₂ = 9∠45⁰

Find
i) √(Z₁ Z₂ )
ii) {(Z₂/Z₁ ) Z₂ }⁴

Learning Outcome 4

Determine the powers and roots of complex numbers using de Moivre's

4) Apply De Moivre's theorem to determine:

a. (-2 + j3)⁵

Use De Moivre's theorem to determine the roots of the given complex numbers in rectangular (Cartesian form) and show the results on an argand diagram:

b. (3 - j4)^(1/2)

c. (-1 - j2 )^(1/3)

Learning Outcome 5

Apply complex number theory to the solution of engineering problems when appropriate

5) A series circuit comprises an inductor of 50 mH, a resistor of 60 ? and a capacitor of 58 µF. A sinusoidal current of 50 mA at 60 Hz flows in the circuit, determine:

a. The inductive reactance
b. The capacitive reactance
c. The impedance of the circuit in rectangular and polar forms
d. The circuit voltage