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Since you are new to the company your line manager is unsure of your capabilities, and has asked you to use the dimensions of P and V to determine the dimensions of R.

Unit Brief

Unit 2/4002: Engineering Maths

Assignment 1: Mathematical Methods and Statistical Techniques

Assignment Number 1 of 3

INTRODUCTION

Task 1) a)

The power (P) dissipated in a resistor (R) which is subjected to a voltage (V) across its terminals is given by the well-known formula;

P = V^2/R 

Since you are new to the company your line manager is unsure of your capabilities, and has asked you to use the dimensions of P and V to determine the dimensions of R.

Voltage (V) = 25v   

Resistance (R) = 20Ω

Current (I) = ?

Ohms Law is V=IR (Unicourse Ltd, 2025) we can transpose the above for I:

I=V/R 

Therefore:

I=25/20 

I = 1.25 A (Amperes, often shortened to Amps, A)

b)

A guitar string, made by your Musical Instruments division, has mass (m), Length (l) and tension (F). It is proposed by one of your junior colleagues that a formula for the period of vibration (t) of the string might be;

 t=2π √  m3l/F

Use dimensional analysis to show your colleague that this formula is incorrect.

As we know from above the dimensions of each variable, we can assume that when the equations are worked, they should be of equal formula both sides to be true.

From the common quantities table encountered in engineering we can assume the following: -

T = time (T)

M = mass (M)

L = Length (L)

F = Force (mass x acceleration) [MLT]

Dimensional analysis

Expression under the square root 

[m3l/F]=(M^3 L)/(M LT-^2 )=M^(3-1) L^(1-1 ) T^2 =M^2 T^2 

Square root the equation

(_^([√ (m^3 l)/F] = √(M^2 ) T^2 =M T)) 

As we can see the equations don`t equal the same outcome and with their calculation theory and the formula is incorrect to prove a period of vibration.

c)

An analogue-to-digital converter (ADC), manufactured by you signals division, takes 15 voltage samples of ramp waveform, measured in mV, as follows ... 3, 6, 9, 12, 15 ... 45.

Your Test colleague has asked you to assist by using a formula to calculate the sum of these 15 voltage samples.

There are a few ways this can be done; the first way is to complete the formula for all the numbers as follows with Sigma notation: -

(_^([√ (m^3 l)/F] = √(M^2 ) T^2 =M T))

We can see that each new term is constructed by adding 3 the previous number and is known as the `common ratio`

No. of samples n = 15

1st Voltage sample a1 = 3mV

Last Voltage sample a15 = 45mV

Sn = n/2 (a1+an)

S 15/2 = (3+45)

S 15/2 (48)

7.5 x 48 = 360 mV

d)

A digital chip, made by your microelectronics division, counts continuously in the sequence: 512, 1024, 2048, 4096, ...

You have been asked to use a formula to calculate the 11th count of the chip

an = a r (n-1) 

a11 = 512 * 2(11-1)

a = 512 x 2^10

a11 = 524,288

e)

A series electrical circuit which you are testing features a capacitor (C) charging via a resistor (R) and a DC supply (Vs). The voltage across the capacitor (Vc) may be described by the equation ...

vc = vs(1-e-t/_/rc) 

Where t represents time

Assuming Vc is 1V after a time of 4 seconds, determine the approx value of the capacitor.

formula working:

vc/vs=1-e^(-t/rc)

e^(-t/RC)=1 - Vc/Vs

C = (-t)/(R1n(1-Vc/Vs))

Voltage (V) = 25v  

Resistance (R) = 20Ω  

Vc/Vs = (1 - e^(-4(20 x 10^(-6) C)))

1/25 = 1 - e^(-4(20 x 10^6 C))

e^(-4(20 x 10^6 C)) = 1 - 1/25

e^(-4(20 x 10^6 C)) = 24/25

C = -4 / (20 x 10^6 ln(24/25))

ln(24/25) = -0.0416666667

C = -4 / (20 x 10^6 (-0.0416666667))

C = -4 / (20 x 10^6 x -0.0416666667)

C = 4 / (0.0833333334 x 10^6)

C = 4 / 83333.334 = 4.8 x 10^(-5)

C = 4.8 x 10^(-5)

C = 4.8 μF

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Understanding Unit 2/4002 Engineering Maths: Mathematical Methods and Statistical Techniques

What Is This Unit About?

The Engineering Maths unit introduces students to the mathematical techniques used throughout engineering practice. Rather than focusing on maths in isolation, this module teaches learners how to apply mathematical principles to solve real engineering problems involving electricity, electronics, mechanics and manufacturing systems. Students are expected to work with dimensional analysis, algebraic manipulation, arithmetic and geometric sequences, exponential equations, and statistical methods that engineers regularly use in industry.

This assignment requires students to demonstrate both mathematical accuracy and engineering understanding. Learners must not only carry out calculations correctly but also explain the reasoning behind each stage, justify formulas used, and interpret results within an engineering context. Many students quickly realise that this unit is very different from school mathematics because marks are awarded for method, presentation and technical explanation as well as obtaining the correct answer.

Why Do Students Struggle With This Assignment?

Many students find this Engineering Maths assignment challenging because it combines several mathematical topics within a single assessment. A learner may feel confident solving simple equations but then struggle when asked to apply dimensional analysis, manipulate exponential capacitor equations, or identify the correct formula for arithmetic and geometric progressions. Switching between different mathematical techniques often causes confusion.

Common areas where students experience difficulties include:

  • Rearranging engineering formulae correctly.

  • Understanding dimensional analysis and SI units.

  • Distinguishing between arithmetic and geometric sequences.

  • Solving exponential equations involving logarithms.

  • Showing clear step-by-step workings to gain full marks.

  • Explaining mathematical solutions using appropriate engineering terminology.

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