tASK 1
A generated AC voltage has a value given by V = 4cos2θ.
You will need to use the identity
a)Find the mean value of the voltage over a full cycle (0 ≤ θ ≤ 2π) using integral calculus
b)Find the r.m.s. value of the voltage over a full cycle (0 ≤ θ ≤ 2π) using integral calculus
This part of the task provides part of the evidence for the grading criterion D2.
TASK 2
A new design of nitrogen charged accumulator, for use in a hydraulic circuit, ( is being factory tested for certification purposes.
The following data has been collected by a technician:
- Gas volume: V = 0.8 m3
- Gas pressure: p = 160 kPa
- Compression index: n = 1.4
- Pressure/volume relationship: pVn= C
- Work done =
Calculate the work done in compressing the nitrogen from 0.8 m3 to 0.6 m3 using:
- integral calculus
- Simpson’s rule
Note: if you wish, you may use a spreadsheet for the numerical method.
This task provides the remaining evidence for grading criterion D2.
guidance notes
Your work should be presented in a tidy and logical order. In particular you should show all of the steps in your calculations and state units. Make sure that you decide on the best units for your answers
TASK 3
Phasor Addition
(i)Two alternating currents are applied out of phase with each other. One is 4 volts and the other is 3 volts 27° out of phase.
These can be written as (4, 0°) and (3, 27°)
Find the result of these voltages as a single combined Polar phasor.
On a graph, plot the 4V phasor in blue.
On the same graph, plot the 3V phasor in red
On the same graph, plot the combined phasor in purple (all between 0° and 360°)
(ii)On the graph that you have drawn in part (x), label the peak voltage on the plot and state its exact value
Task 4
A company produces microchips. It has some in storage and produces 34 an hour. After 1 hour it has a total of 3428 microchips
i)How many chips will the company have a week later, assuming the production continues 24 hours a day?
This part of the task provides part of the evidence for the grading criterion P2.
ii)An order is put in for 13,526 chips. In days and hours, how long will it take before the order can be met?
This part of the task provides part of the evidence for the grading criterion P2.
task 4b
Another company is making microchips on a new machine and on day one it produces 400 microchips. On day two it produces 420, on day three 441 and so on as the process is streamlined.
If the process continues to increase in speed at this rate:
i)How many chips will be produced on day 23?
This part of the task provides part of the evidence for the grading criterion P3.
ii)How many chips in total will be produced in the first 20 days?
This part of the task provides part of the evidence for the grading criterion P3.
As the company is bringing in its new machinery it is phasing out another. This one produces 300 on day one and 200 on day two.
iii) Assuming this follows a geometric pattern to infinity, what is the maximum number of chips
in total that can be made?
Task 5b Two voltages combine to form a new one modelled by
V = 7sinωt + 9cosωt
Find the combined voltage and the phase shift “φ”