Q1. Sketch with labelled axes the voltage signal (units Volts) described by the function,

V(t) =   cos (2π  ∙ 100 t − ) ,  for t = 0 to 0.02 seconds.

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Q2.  Calculate the differential of the following voltage function (units Volts) and hence calculate the rate of change of the voltage at t= 2 seconds,

V(t) =  3 e −  t cos (3πt − ) .

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Q3. Calculate the indefinite integral of the following voltage signal,

V(t) =  cos (10πt − ).

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Q4. The current charging a capacitor with a capacitance of 500 µF is described by the function I(t) =  3e−  t  mA. Assuming no charge on the capacitor at t=0, calculate the  charge on the capacitor when t = 0.4 seconds.

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Q5. Sketch with labelled axes a frequency representation V(f) of the following voltage signals,

a)      V(t) =   cos(100 t),

b)      V(t) =  cos(4000 t) ∙ cos(314159 t) .

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Q6. Solve for U1 , U2  and U3  the following simultaneous equations using Gauss Elimination, showing each step of your calculations,

( 3        ) () = () .

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Q7. Calculate the total complex impedance between terminals A and B in the circuit shown in Fig Q7 below. Give your solution in both Cartesian and polar form.

- j 3 Ω

j 4 Ω

Figure Q7

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Q8. An ideal voltage source is connected with one resistor, one capacitor, and one inductor as shown in Fig. Q8 below. The source provides an ideal sinusoidal voltage Vs  = 5V (RMS) of frequency f = 50Hz. Underlined quantities are phasors.

-j1Ω

Figure Q8

a)  Calculate the combined admittance YLR of the resistor and inductor, and the   total impedance ZCLR of the resistor, inductor, and capacitor, presented to the voltage source.

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b)  Using nodal analysis or any other method, and taking VS as the reference phasor, calculate the phasor voltages VLR, and VC  .

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c)  Draw a phasor diagram which clearly indicates that  VS  = VC  + VLR .

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