ELET1200 – Basic Circuit Analysis Study Notes

ELET1200 – Basic Circuit Analysis Notes

Course Information

  • Course Code: ELET1200
  • Date: Monday, 23rd March 2026
  • Assignment Due Date: 11:59 p.m. Friday, 3rd April 2026
  • Assignment Number: 2
  • Instructions: Show ALL working.

Assignment Details

Question 1: Sinusoidal Current and Voltage
  • Given Information:
    • Maximum current (): 15 A
    • Period of current: 2 ms
    • Maximum voltage (V): 45 V
    • Phase difference between voltage and current: (\frac{\pi}{2})
    • Period of voltage: 2 ms
a) Graph Sketching
  • Task: On a single labelled graph, sketch both sinusoidal waveforms (current and voltage).
  • Key Identifiable Features to Include in the Graph:
    • Current waveform characteristics:
    • Maximum amplitude: 15A
    • Time period: 2ms
    • Voltage waveform characteristics:
    • Maximum amplitude: 45V
    • Time period: 2ms
    • Phase lag of (\frac{\pi}{2}) (90 degrees) behind the current.
  • Note: The graph should be sketched by hand, ensuring clarity in identifying key points and phases.
b) Curves Values at Specific Time
  • Determine values of current and voltage at t = 0.6 ms and t = 1.2 ms:
    • Formulas to Use:
    • Current: [ I(t) = I_{max} \sin(\omega t) ]
    • Voltage: [ V(t) = V_{max} \sin(\omega t - \frac{\pi}{2}) ]
    • Where: (\omega = \frac{2\pi}{T}) and (T = 2 ms)
    • Calculations:
    • Calculate (\omega):
      [ \omega = \frac{2\pi}{2\times 10^{-3}} = 1000\pi \, rad/s]
    • At (t = 0.6 ms):
      • Current value: [ I(0.6) = 15 \sin(1000\pi \cdot 0.6 imes 10^{-3}) ]
      • Voltage value: [ V(0.6) = 45 \sin\left(1000\pi \cdot 0.6 imes 10^{-3} - \frac{\pi}{2}\right) ]
    • At (t = 1.2 ms):
      • Current value: [ I(1.2) = 15 \sin(1000\pi \cdot 1.2 imes 10^{-3}) ]
      • Voltage value: [ V(1.2) = 45 \sin\left(1000\pi \cdot 1.2 imes 10^{-3} - \frac{\pi}{2}\right) ]
c) Time to reach 25V
  • Determine at what time voltage reaches 25V:
    • Use Voltage Equation: [ V(t) = 45 \sin(\omega t - \frac{\pi}{2}) = 25 ]
    • Rearranging gives [ \sin(\omega t - \frac{\pi}{2}) = \frac{25}{45} = \frac{5}{9} ]
    • Solve for (t):
    • [ \omega t - \frac{\pi}{2} = \arcsin\left(\frac{5}{9}\right) ]
    • Plugging back in gives time at which voltage reaches 25V.
Question 2: Circuit Analysis Using Figure 1
  • Figure Reference: Analysis based on provided circuit diagram (identified as Figure 1).
a) Total Circuit Impedance ZT
  • Task: Determine total circuit impedance (ZT).
    • Analysis Requirement: Show working for calculating ZT based on circuit arrangement and components in Figure 1.
b) Total Current IT
  • Task: Calculate total current (IT) flowing in the circuit.
    • Analysis Requirement: Use Ohm's law and knowledge of circuit configurations to derive current value based on ZT and source voltage.
c) Currents I2 and I4
  • Task: Calculate individual currents I2 and I4 in the circuit.
    • Presentation: State values in both rectangular and polar forms.
    • Mathematical Representation:
    • For Rectangular Form: [ I = A + jB ]
    • For Polar Form: [ I = R\angle \theta ]
d) Current Phase Relationships
  • Determine the phase relationship of currents I2 and I4 with the source voltage:
    • Options: Each current can be leading, lagging, or in phase based on the respective circuit impedance and voltage source's phase.
e) Voltage Divider Rule
  • Task: Use the voltage-divider rule to determine the voltages across components R1, XL1, R4, and XC2.
  • Formula for Voltage Divider Rule:
    • For resistors:
      [ V_n = V_{total} \frac{Z_n}{Z_{total}} ]
    • Where (V_n) is voltage across the component, (Z_n) is the impedance of the component, and (Z_{total}) is total impedance.