# Questions tagged [calculus]

Anything related to (differential and integral) calculus, i.e. the branch of mathematics concerned with the manipulations of infinitesimally small quantities. Concepts from calculus are often used in engineering to build more complex and accurate models of physical systems than those which can be built using basic algebra alone.

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### How to derive a generalized equation with respect to time for voltage across the inductor & current in an RL circuit with a DC PWM source?

Circuit connection: I have this resistor (96 Ω)-inductor (990 µH) circuit connected to a PWM source of frequency 62.5 kHz; And ...
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1 vote
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### Getting temperature dependence for a beta multiplier circuit

I am currently working on designing a beta multiplier voltage reference, and came across this paper. I am slightly confused as to how they ended up with equation (6) after taking the derivative of (5) ...
1 vote
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### Discrete Fourier transform for musical analysis

I am a senior in highschool and am currently trying to conduct an exploration on Fourier analysis, specifically using the discrete Fourier transform to analyze a chord played on my piano. Basically I'...
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### Can Watt’s law be derived from the Ohm’s law without using calculus?

Unlike Ohm’s law Watt’s law is not a fundamental law of electronics, as it can be derived from other fundamental laws of electronics. In the derivation above (see the pic) I used definition of current ...
422 views

### Finding Vrms over time

The plot of voltage over time is given in below plot. As you can see, $V_{max}=2v \text{ and } V_{min}=0v$ $t1=2ms, t2=8ms, t3=5ms, \text{ and period, } T = 15ms$ Question is to find $V_{rms}$ ...
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### Please explain solution (TEM waves in spherical coordinates)

I have a question and a solution, I don’t know how the solution came up with the variables and values highlighted in blue in the solution part. Question: Solution:
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### How can an ideal motor do any work when the average of instantaneous power over one cycle is zero? [closed]

The attached screenshot illustrates the instantaneous power delivered to a purely inductive load as a function of time. How does an ideal motor (or perhaps some other purely inductive load) do any ...
1 vote
400 views

### How to calculate total power required for an electric vehicle (ebike) design?

I wanted to design an ebike with good enough specs to satisfy my requirements, my first consideration was the power required to move the bike at my required speed and from there I can choose a motor. ...
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### Transient Response, State Response, and Zero-Input/Zero-State, Natural and Forced

I would just like to know if each of these "responses" are the same. Are the words being used just synonyms of each other? Steady State and Transient Natural and Forced Zero-Input and Zero-...
1 vote
93 views

### In-Series current source equation solving

I'm an electronic newbie, i was simulating this circuit on LtSpice and i found the result below, i tried with different methods (Kirchhoff's laws, Millman theorem, superposition) but i failed to have ...
1 vote
277 views

### Fourier Transform Time Scaling Property using f (frequency) or w (omega - angular frequency)

The time scaling property for a fourier transform is as follows: My book shows this property in terms of $f$; however, my instructor likes to use $\omega$. I have also seen this property written ...
244 views

### Capacitor constant power charge, constant current discharge curve

I have an (ideal) capacitor that is simultaneously being charged through a DC/DC boost converter (assumed constant power $P_{in}$) and discharged through a linear regulator (assumed constant current ...
1 vote
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### How to calculate kWh from amps

I'm getting measurements from an IoT device. This measurements are in amps (I get one every 2 min or so). I know the voltage of the device. From what I've seen online I can calculate the power in ...
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### How to find mean value of square signal

I have a comparator circuit and I need to find the mean value of the output square wave. I have calculated it like this: $Vmean=1/T*integral(U*dt)$ from 0 to T and I got $Vmean=-0.7896V$ Can ...
2k views

### How to express a function in terms of singularity functions?

This is the question from the domain of the operational calculus related to circuit analysis. Here is the graph of the sawtooth function: It is asked to represent this function as a combination of ...
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### Calculate U(t) when capacitor C1 charges C2 via a resistor R

simulate this circuit – Schematic created using CircuitLab The switch SW1 is activated at t=10s and charge from C1 is transferred to C2. The power supply charges continuously with 1kV 1mA. How ...
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### Capacitor sizing for known current load

Apologies in advance for the long question, but I've hit a dead end trying to work through an interesting capacitor sizing problem. I'm hoping someone here can help. Problem Description I have a ...
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### Voltage calculation for the schematic [closed]

I would like to know how to calculate the output voltage for the following schematic. I would also like to see the calculations step by step. Right now I am not able to do this, I'm kind of new in ...
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### Heating time of an aluminum plate

I'm designing a circuit for my 3D printer's aluminium heating plate (200x200 mm) and I wanted to be sure before buying resistors. Also, I'm using a Sanguinololu 1.3a. I want it to heat at 120° fast. ...
In my Nilsson "Electric Circuits, 5th ed" book, there's this drill exercise near the beginning of the book. Here it is: Current at the terminals of the element is t<0: $$i=0$$ t>=0: ...