Qualitative Questions About University Circuits Quiz

Answer: You should never connect multiple current sources in series

Most people are familiar with voltage sources, which supply a specific voltage (eg. batteries), and can have the current change as needed. Current sources also exist, which supply a specific current and can change their voltage.

Because a node can only have one voltage, it is dangerous to connect two different voltage sources together in parallel. Similarly, because a wire can only have one current at a time, it is dangerous to have two different current sources together in series.

A voltage in a circuit can safely go lower than ground (and often does). You can also safely add voltage sources together in series, even if one is DC, and the other is AC.

Answer: A circuit with a resistor and voltage source in series

When students are given a circuit with a bunch of resistors and one or more batteries, and asked to find the equivalent resistance, they are finding the Thévenin equivalent circuit. If the simplified circuit is instead represented with a resistor in parallel with a current source, it is called the Norton equivalent.

Engineers often learn about circuits first before moving onto the more general control theory. To illustrate that the math is the same, often engineers will study spring-mass-friction systems, with springs acting like capacitors, masses acting like inductors, and friction acting like resistors.

Answer: Connecting the output to the input with a feedback loop

An op amp has five terminals: two inputs (inverting and non-inverting), one output, and two power terminals (positive and negative). If the non-inverting input is a higher voltage than the inverting input, then the output will be the positive power supply voltage. If the inverting input has the larger voltage, then the output will be the negative power supply voltage. If the two inputs are the same voltage (or very close to it), the op amp will be in the linear region.

When a feedback loop is added, connecting the output of the op amp to one of the inputs (often with a resistor or capacitor), then the op amp acts like it has "a virtual short" between the two inputs, making them the same. This principle is used extensively when studying circuits with op amps.

Answer: A filter

In DC circuits, a capacitor looks like a break in the circuit. To an AC circuit, a capacitor looks like a short (just regular wire). A regular wire means to two nodes on either side are actually the same node, and thus, always have the same voltage.

If you are using a power supply that is supposed to provide a steady voltage, but in reality it is a little noisy, then you can use a capacitor and the law of superposition to solve your issue. The noisy output can be treated as two different signals: a nice steady DC signal, with a noisy AC signal added on top of it. When the capacitor is added between the output and ground, the DC part sees it as an open circuit, and is not affected, but the AC part sees it as a short. Because the AC part is directly connected to the ground, it is forced to be 0V, removing the noise from the output.

The capacitor is filtering out the high-frequency noise (making it a low-pass filter). These capacitors are quite common, and are called bypass capacitors.

Answer: Five time constants

The equation for a discharging capacitor is v(t) = Vc×e^(-t/RC), where t is the time, Vc is the original voltage, R is the resistance, and C is the capacitance. When you multiply resistance and capacitance you get time, so the RC part is called the "time constant". If you wait five time constants, the capacitor's voltage will be less than 1% of its starting value, which is low enough to consider it fully discharged.

Resistors and capacitors come in a large range of values, but if you used a 10 kΩ resistor (a middle-range value) and a 1 μF capacitor (a middle-range value), then the time constant would be 10 milliseconds, so it would take 50 milliseconds to discharge the capacitor.

The same principal and time constant are used when charging a capacitor. Resistor inductor (RL) circuits have very similar math, but in those circuits the time constant is L/R.

Answer: A component that resists changes in current

Physically, inductors and capacitors may seem very different, but to an engineer there are many similarities and mirrored functions.

An inductor will resist changes in current, and will generate voltages to make that happen. Similarly, capacitors are devices that resist changes in voltage, and will generate the necessary currents.

In a DC circuit, a capacitor will look like an open circuit, and an inductor will look like a short. In an AC circuit, a capacitor will look like a short, and an inductor will look like an open circuit.

A diode is a component that lets current flow in only one direction.

Answer: The Laplace transform

The Laplace transform is very useful, but can only be applied to certain circuits in certain situations. It is not a magic bullet to solve all circuit problems.

Most people are more familiar with the Fourier transform, which is actually a special case of the Laplace transform. The Laplace transform uses the whole imaginary plane (numbers can have real parts and imaginary parts), while the Fourier transform is only concerned with the imaginary axis (numbers are purely imaginary, with no real component).

The Laplace transform is for continuous (analog) functions. For discrete (digital) functions, the Z-transform is used, and has an analogous Discrete Fourier Transform.

De Morgan's laws are used when solving logic problems, and the Gamma function is used in mathematics and statistics.

Answer: Because i was already used for current

Isn't capital I used for current? Usually, yes, but when you start making the distinction between current in different domains, small i is used for time-domain, and capital I is used for s-domain. Voltage is treated the same way (v and V).

So because small i was already used, engineers decided to use the next letter, j, for the imaginary constant. Even in fields not about circuits, if it falls under the engineering umbrella, the imaginary unit is always j.

And for those wondering why I was used for current, in the original French, it was for "Intensité du Courant". And then C was used for capacitance. And because I was used for current, they decided to use L for inductance (in honour of Lenz).

The German word for "imaginary" is "imaginäre" (which does not start with j).

Answer: Impedance

Impedance is measured in Ohms, and has a real part (Resistance) and an imaginary part (Reactance). When moving from the time-domain to the s-domain, the different components are changed as follows:

R → R
L → Ls
C → 1/Cs

Because resistors stay real, and capacitors and inductors become imaginary, when you mix them together you get complex numbers with both real and imaginary parts.

Engineers also take delight in naming the reciprocal of various measurements. Here are some common measurements and their reciprocals:

Impedance - Admittance
Resistance - Conductance
Reactance - Susceptance
Capacitance - Electrical elastance

Answer: dBm

dB stands for "decibel", which most people are familiar with when using their stereos. dB just measures relative signal strength. Turning up your music by 10 dB will make it 10 times louder.

dB is useful for measuring the relative gain of a signal, but not its absolute power. dBm is decibel relative to one milliwatt, and is an absolute measure used in many industries. 0 dBm is 1 mW, 20 dBm is 100 mW, and -20 dBm is 10 μW. Most Bluetooth devices output around the -46 dBm (25 nW) range, but the signal gets weaker the father you move away from it. The lower limit is usually around -90 dBm (1 pW).

Kilowatts hours (kWh) are how power companies often measure electricity usage. Pounds per square inch (PSI) is a non-metric unit of pressure. The British thermal unit (BTU) is another unit of energy. It is calculated the same way a calorie is, but instead of being the energy required to raise one kg of water one degree Celsius, it is the energy required to heat one pound of water by one degree Fahrenheit.