Qualitative Questions About University Circuits Quiz

Quiz Answer Key and Fun Facts

1. Without any power sources, circuits would be a pretty boring pile of wires and components. When adding a power source to a circuit, you should be thinking about safety. Which of the following statements about power sources is true?

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.

2. A resistive circuit is a circuit with only resistors and power sources. If you were given a circuit with a bunch of resistors, and asked to find the Th�venin equivalent circuit, what would it look like? Hint: many high school physics students probably already know how to do this, though maybe not by this name.

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 Th�venin 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.

3. A common circuit element that students are introduced to early is the operational amplifier (op amp), which compares two inputs and changes the output accordingly. The op amp has three modes of operation: positive saturation, negative saturation, and the linear region (the most interesting part). The linear region is difficult to stay in naturally, so what method is usually used to force the op amp to operate in the linear region?

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.

4. When using a power supply to power a circuit (instead of a battery), engineers will sometimes place a capacitor between the output and the ground. What is this capacitor acting as?

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.

5. When a source is taken out of a resistor capacitor (RC) circuit, the capacitor discharges following an exponential function (similar to Newton's Law of Cooling). Mathematically, this means a capacitor will never be fully discharged. Engineers don't have infinite time to wait, though, so how long is "long enough" to consider the capacitor discharged?

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.

6. If you asked a physicist what an inductor was, they would tell you it's a coil of wire, and might mention names like Faraday and Lenz. For an engineer building a circuit, though, what is an inductor?

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.

7. Engineers have a secret: we are actually quite lazy. Adding capacitors and inductors to a circuit means we have to start using calculus, which is hard. To get around this, Engineers will move from the time-domain to the s-domain, where calculus becomes algebra (much easier). What is the name of the process used to move from the time-domain to the s-domain?

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.

8. In the s-domain, the calculus goes away, but complex (imaginary) numbers are added. In most fields of study, the letter i is used to denote the imaginary unit. Why did engineers decide to buck the trend and use the letter j instead?

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 "Intensit� 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 "imagin�re" (which does not start with j).

9. In the real world, the resistance of resistors, capacitance of capacitors, and inductance of inductors all have different units and cannot be added together. But in the s-domain they can be added together because they all a single measurement called what?

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

10. A major component of studying circuits is how they propagate and manipulate signals. In the real world, signals can exist across such a massive range of strengths that a linear measurement is not practical. Instead, engineers and people in any field involved with signals will often use which logarithmic unit to measure signal strength?

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.

Source: Author qrayx

This quiz was reviewed by FunTrivia editor rossian before going online.
Any errors found in FunTrivia content are routinely corrected through our feedback system.

In university I had to take a few courses on circuits. It's been a while, but here are some qualitative questions about circuits. I promise that you won't have to do math in this quiz.

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