# Tutor profile: J Z.

## Questions

### Subject: Physics (Electricity and Magnetism)

Where do you most commonly see the interplay of electricity and magnetism?

The interaction/interplay of electricity and magnetism is most evident in electric motors. These motors are found in everyday objects such as a (battery powered) toy car or the vegetable chopper in the kitchen or the flying drones that are so popular these days. These motor are based on Faraday´s principle which describes that a coil of wire exposed to the changing magnetic field will generate a voltage across its terminals or conversly a coil of wire moving in a magentic field will have a voltage generated across its terminals. As long as there is a relative change in the magentic field across the coil (due to movement of the coil or the change in the magnetic field strength) a voltage will be generated. Now if the terminals of the circuit are closed via a circuit a current will be produced and its resulting magnetic field will interact with the original magnetic field (to either repel or attract) and motion is the result.

### Subject: Applied Mathematics

Can you give an example of the real-world application of the integral function ?

I will give you two ! The integral function or integration can be successfully used: 1) to characterize the behaviour of the (ideal) capacitor, one of the primary (building block) components used in almost every electrical circuit. As we know the capacitor is a device used to store energy, in the form of electrical charge, which is indicated by a voltage across the terminals of the capacitor. How can one capture this behaviour? Well, if you integrate the current (electrical charge) flowing through the capacitor over a period of time, it will give you the voltage change across the capacitor terminals. 2) in industrial Proportional-Integral-Differential (PID) controllers. Let´s say, one has a desired (setpoint) value for a physical parameter (e.g. temperature of a chamber) and a measured value of the same parameter. Let´s then consider, there is a constant/continuing difference between the desired and the measured temperature values, in the steady-state (stable/at rest) operating condition of the chamber. Now, an error signal (generated by subtracting the measured value from the desired value) can be provided as input to the PID controller. The controller samples of this error signal and integrates it to increase/decrease the heat generated by the heating system of the chamber. When the error signal (the temperature difference) reduces to zero, the effect of integration function stops, and the output of the heating system is kept at that value to maintain the temperature onwards.

### Subject: Electrical Engineering

What physical significance does a root-mean-square (RMS) value of an AC signal/waveform have and where can its effective use be seen commonly in electrical engineering?

AC signals/waveforms can be of different shapes such as sinusoidal, square, triangular or other alternating shapes etc. How do you then, for example, compare a sinusoidal signal against a triangular signal, when both have the same peak value or indeed compare between an AC and a DC signal? It then must require more parameters to capture the difference. RMS provides a single value (a parameter) which can be used to compare between different AC signal/waveforms and AC and DC. In a physical sense, it is exactly the same heat that would be (caused to be) generated in a resistor by two equivalent AC signals (current or voltages) or a DC and its equivalent AC signal. The use of the RMS value can be most effectively seen in a True-RMS measurement meter, available in markets, which takes into account the actual shape of the AC signal (by calculation using the sampled values of the signal and the mathermatical expression for the RMS); rather than assuming a AC signal is of sinusoindal shape and therefore the RMS value is sqaure-root 2 of its peak value.

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