(a) An AC voltage is described by the equation 푣 (푡) = 푉cos(휔푡 + 휙). Sketch this voltage waveform, and explain the meaning of terms 푉, 휔, 푡 and 휙.
Sketch of the voltage waveform.
V The maximum or peak value of the voltage
휔 the angular frequency expressed in radian per seconds obtained from frequency using the formula
t time in seconds
휙 The initial phase velocity in radians or degrees. This quantity determines value of cosine wave at time t=o
(b) A sinusoidal voltage source with a frequency of 175 Hz and a peak-to-peak amplitude of 10 V is connected to a 700 Ω resistor.
i) Calculate the average power dissipated by the resistor.
For average power dissipate
Hence
Where V=
ii) Calculate the RMS current that flows in the circuit.
For the rms current Irms,
Alternatively,
Question 2
(a) Write down expressions for the complex impedance of an inductor and capacitor in terms of the angular frequency, 휔.
For an inductor where L is the inductance of the inductor in Henry
For a capacitor where Cis the capacitance in Farads
(b) Using j-notation obtain an expression for the impedance of circuit shown in Figure Q9(b) between points A and A′ in terms of R1, R2, L and C at an angular frequency of 휔.
From the diagram, L and are in series. The effective series resistance is in parallel with
The effective parallel impedance is in series with C
For L and series, Z=
Z//
Total impedance seen by port A-A’
(b) Hence or otherwise, determine the magnitude and phase of the impedance between points A and A′ if R1 =R2 =100Ω, C = 500 μF and L=100 mH and a frequency of 휔 = 103 rads-1.
Substituting the values
Rationalizing each term
Question 3
Find the Thévenin equivalent circuit seen by the load resistor RL for the circuit below.
In order to calculate thevenin resistance the voltage source is short circuited while the current sources are open circuited.
Looking back into the circuit from the load end,
50//120, the result in parallel with 50 whose result is in parallel with 30. The effective resistance is in series with 15. The result is in parallel with 5 and the final result in series with 2 resistor
In series with 15
In series with a
To calculate the Thevenin voltage , replacing the current sources with their equivalent voltage sources,
And using Kirchhoff’s voltage law to solve for a loop current through 5resistor,
Since no current flows through the 2 the thevenin voltage is equivalent to the voltage across the 5 resistor
Thevenin equivalent circuit
