1. Determine the required ratio ofT to give the waveform of FIGURE 1 a r.m.s. value of 4 volts.

2. In the circuit of FIGURE 2, the generator VI has a voltage of 120 volts (r.m.s.) @ 60 Hz and generator V2 has a frequency of 50 Hz. The load is represented by an inductor of 0.1 I-1 and a resistor of 2052.

(a) Determine the r.m.s. voltage of V2 if the reading on the ammeter, which reads true r.m.s, is to be 5 A.

(b) Calculate the power factor of the load for the conditions set in (a) above.

3. Determine if the functions below are odd, even or neither.

(a) fix) = A.2 + 2

(b) fix) = (x2 + 2)tan(x2)

(c) fix) = (x2 + 2)sin (x)tan(x2)

4. Determine the Fourier series for the function;

(0, for-2 <0 j(1) = r, for 0 t < 2

5. Harmonic distortion is a serious problem for the electrical supply industry and can cause overheating of induction motors and transformers and cause the neutral conductor to carry more than its rated current.

Harmonic distortion is caused by consumer loads requiring non-sinusoidal currents. There are two main types of load that generate harmonic currents:

• Computers and other office equipment. The typical waveform of the current taken by such devices is shown in FIGURE 3(a).

• Variable speed motor drives as used in the manufacturing industry and in lifts. A typical current waveform of such loads is given in FIGURE 3(b).

The table on page 6 gives the complex Fourier coefficients obtained from a load's current waveform (this data set is available on a spreadsheet on the CD-ROM (EEP TMA3 v2.1 Q5)).

(a) Use Excel's Fourier Analysis 'inverse' function to transform the complex coefficients back to the original time domain values.

(b) Use the time domain values to plot a graph of the waveform and hence state if the waveform is from a TYPE A or TYPE B load (as per FIGURE 3).