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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

    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

    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

    Homework Statement What is the current in this circuit: [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

    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

    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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    What if it is all wrong?

    How do we know that all we think we know about the universe is correct? The whole universe could be COMPLETELY different from what we perceive. You might say that you can do experiments which show certain things, but what if the experiment observations fit this picture we have built up, however...
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    Antimatter colliding with matter

    I read somewhere that if a particle of antimatter collides with a particle of matter, they annihilate each other. Maybe this is because of what is happening in the 4th dimension(time). Since antimatter is matter traveling backwards in time, maybe the two particles stop in the 4th dimension...