# Complex Numbers

Paper, Order, or Assignment Requirements

Part C and Part D to be completed> Some understanding of circuits with inductors, capacitors and resistors included would be helpful.

PART B

• Show graphically, how Voltage and Current vary with time in the circuits shown below.

• Explain mathematically what is meant by the terms “in phase” and “out of phase” as they relate to Voltage and Current in the circuits above, and then explain how the use of complex numbers assists the overall calculation of impedance for RLC circuits.

PART C           (KAPS/MAPS: Complex Routine and Non-routine)

A cross over system for speakers uses capacitors and resistors to channel different frequencies of music to different speakers. The “woofer” reproduces low frequency sounds best. The “mid-range” speakers reproduce sound in the voice range best and the “tweeter” reproduces high frequency sounds best.

Using MS Excel, produce graphs of impedance versus frequency for the three speakers shown below.  Demonstrate your understanding of each model by explaining it in context.

PART D          (MAPS: Complex Non-routine)

The three types of speakers mentioned above are usually housed in the same cabinet, fed by the one lead from the amplifier. They are connected in parallel as shown.

It is important that the total impedance of the speaker box does not vary too much or fall significantly below 8 Ω. Therefore, it is a requirement for maximum sound production is that the total impedance keeps to between 6Ω and 10 Ω.

Investigate the frequencies that are used for sound reproduction, decide on reasonable ranges for cross over frequencies and calculate the values for the inductors and capacitors shown, explaining your reasoning.The range of total impedance of the speaker boxes is best shown on an ‘impedance versus frequency’ graph. You must submit an electronic copy of your spreadsheets.