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EG3007 Engineering Analysis And Methods 1

tag 0 Download1 Pages / 37 Words


Learning Outcomes:

Analyse and model engineering situations and solve problems using trigonometric methods.

Analyse and model engineering situations and solve problems using complex number and phasor diagram methods.

  1. FIGURE 1 shows the positions of four towns marked on a map.
  • Calculate, to the nearest kilometre, the distance between towns Wand Y.
  • Calculate, to the nearest degree, the size of the angle marked θ.
  • Calculate, to the nearest kilometre, the distance between towns Yand Z.
  1. The instantaneous value of current, iamp, at t seconds is given by:

i = 15 sin(100πt + 0.6)

Find the value of

  • The amplitude.
  • The period.
  • The frequency.
  • The initial phase angle (when t= 0), expressed in both radians and degrees.
  • The value of iwhen t = 2.5 s.
  • The time (in milliseconds) when the current first reaches its maximum value.
  1. Use the trigonometrical identities to expand and simplify if possible.
  • (i)  cos(270° – θ)
  • sin(270° – θ)
  • cos(270° + θ)

(b) The voltage V1 and V2 are represented by as follows,

V1  = 3sin(ωt)

V2  = 2 cos(ωt)

If V3 is the sum of V1 and V2,


Find the expression of V3 in sine waveform V3  = R sin(ω t + α )

and verify that the resultant voltage V3 is in the same frequency as V1 and V2.

  1. (a) Given the equivalent impedance of a circuit can be calculated by the expression

Z = Z1Z2/Z1+Z2

If Z1 = 4 + j10 and Z2 = 12 – j3, calculate the impedance Z in both rectangular and polar forms.

  • Three impedances are connected in parallel, Z1= 2 + j2, Z2 = 1 + j5 and Z3 = j Find the equivalent admittance Y


Express the admittance in both rectangular and polar forms.

  1. The potential difference across a circuit is given by the complex number
  • = 40+  j35 volts and the current is given by the complex number
  • = 6+  j3 amps
  • Sketch the appropriate phasors on an Argand diagram.
  • Find the phase difference (i.e. the angle φ) between the phasors for voltage Vand the current I.
  • Find the power (watt), given that

power = |V|  × |I|× cos( φ)

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