In an LCR circuit (circuit with inductor, capacitor and resistor), are the following statements always true?
The capacitor voltage always lags the resistor voltage by a phase difference of 90°.
The inductor voltage always leads the resistor voltage by a phase difference of 90°.
Sorry I should have explained it better. When you rearrange the equation, you get the x and dx on one side, and the y and dy on the other side. Do you have to make each side an integral? E.g. does it have to be ∫x dx = ∫y dy, or can you rearrange to x dx = y dy? If you can, what does the...
If you have a differential equation with variables separated, such as dy/dx = 4x2/3y3, and you rearrange it to 3y3 dy = 4x2 dx, what does the dy/dx mean in this case, and can you even rearrange it like that or must you do this: ∫3y3 dy = ∫4x2 dx ?
I never really understood leibniz notation. I know that dy/dx means differential of y with respect to x, but what do the 'd's mean? How come the second-order differential is d2y/dx2? What does that mean? And what does d/dx mean?
Solve the equation √(6 + 3√2) = √a + √b, writing a and b in the form a + b√c.
In the answers they say that a + b = 6, but I cannot see how they can say this.
The Attempt at a Solution
I square both sides, and that is as far as I get:
6 + 3√2 =...
I'm getting confused with EMF, terminal voltage and internal resistance etc... isn't the 1.5V the EMF, which means that the actual potential rise (terminal voltage) will be less that 1.5V?
If I were to add up the EMFs, I would be assuming no current is flowing.
What is the current in this circuit:
All potential differences in a closed portion of a circuit must add to 0.
Terminal Voltage = EMF - I x internal resistance.
The Attempt at a Solution
I do not...
Well I factorise it to this k(k - 16) < 0 then what? I tried dividing both sides by k, then I get k < 16 but how can I divide both sides by k as I don't know if its positive/negative? And how do I get the 0 < k?
But I'm not letting z = a + ib. I am simply trying to find all the pairs of a and b that satisfy the equation (a + bi)2 = 48 + 14i
The way I think of it, is that the expression in brackets (a + bi) is not a complex number, its a number (real, imaginary, or complex) added to another number (real...
Why are a and b assumed to be real? It doesn't say anything about that in the question, and if you substitute the imaginary solutions into the original equation, it works. (e.g. the solution a = i, b = -7i works)
Thank you, that makes it a bit easier.
In the answers for that question, they go from a2 - b2 = 48 to the solutions. It seems they are skipping a lot, so that's why I thought there must be an easier way.
Find all pairs of values a and b that satisfy (a + bi)2 = 48 + 14i
2. The attempt at a solution
I managed to solve it, but it took a while and I was wondering if there is an easier/quicker way.
What I did was expanded (a + bi)2 into (a2 - b2) + 2abi
From there, I can...
Checking solutions -- textbook wrong about roots?
If I have the equation sqrt(3x + 1) = x - 3 and I need to solve for x, by squaring both sides then solving the resulting quadratic, I get the solutions x = 1, 8
However, since I squared the equation, I need to check if the solutions are...