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    Phase in LCR circuits

    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°. The current...
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    Leibniz notation

    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...
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    Leibniz notation

    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 ?
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    Leibniz notation

    So the second derivative should really be d2y/(dx)2?
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    Leibniz notation

    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?
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    Solving √(6 + 3√2) = √a + √b

    So you would also be able to say that a + 2√(ab) = 6 and b = 3√2, and solve that way (with the risk of it being horribly complicated)?
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    Solving √(6 + 3√2) = √a + √b

    Ah, ok. So there would be many other solutions, and they are only finding one such solution?
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    Solving √(6 + 3√2) = √a + √b

    Homework Statement Solve the equation √(6 + 3√2) = √a + √b, writing a and b in the form a + b√c. Homework Equations 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 =...
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    Circuit with two cells

    Thank you for your time :biggrin:
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    Circuit with two cells

    Aha! So the net EMF is what creates a current in a closed circuit or part of a circuit? And the net EMF in this circuit is zero so the current will also be zero? :D
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    Circuit with two cells

    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.
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    Circuit with two cells

    Sorry, I have added them in.
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    Circuit with two cells

    Homework Statement What is the current in this circuit: http://img802.imageshack.us/img802/4646/8ekh.png [Broken] Homework Equations 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...
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    Solving inequality with different power variables

    Ok, so if I say k < 0 (case 2), then when I divide both sides by k I flip the sign. Then I get k > 16 ?????
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    Solving inequality with different power variables

    Ok, then I get k < 0 and k < 16, but it should be 0 < k < 16
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    Is anyone else feeling the same?

    Most people would know Newton and Einstein. Not many would know Kaku. What has he done?
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    Solving inequality with different power variables

    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?
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    Solving inequality with different power variables

    Homework Statement Solve for k: k2 - 16k < 0 In the answer it has 0 < k < 16, I do not know how they get there from the original question.
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    Finding all pairs of values that satisfy complex equation

    Ok so the textbook is wrong in having the imaginary solutions?
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    Finding all pairs of values that satisfy complex equation

    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...
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    Finding all pairs of values that satisfy complex equation

    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)
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    Finding all pairs of values that satisfy complex equation

    Nice idea, but does that get the complex solutions? I tried it and it didn't seem to...
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    Exponential functions word problem

    Is the exponent (1/10)t or 1/(10t) ? Also you can press the little X2 button to do exponents properly.
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    Finding all pairs of values that satisfy complex equation

    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.
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    Finding all pairs of values that satisfy complex equation

    Homework Statement 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...
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    Checking solutions - textbook wrong about roots?

    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...
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    PF Random Thoughts Part 2

    Let's rebel against this, every time you view this thread, also load up the original thread and refresh it a few times to add to server load. :rofl:
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    What if it is all wrong?

    Prove it. I could be imagining you saying it. Then again, you could be imagining me saying this.
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    What if it is all wrong?

    Yeah, I sometimes wonder whether anyone else even exists, maybe I am imagining the whole world somehow. Those of you who exist, please raise your hand now :3
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    What will replace silicon chips?

    Your car can only go the speed limit? Pblackf
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