Field of NoThingness - spl BiNal

Given, Potential $V = 300\;V$ Capacitor $C_1 = 3\mu F$ Capacitor $C_2 = 6\mu F$ Energy stored in each capacitor $E = ?$ When the capacitors are connected in parallel, then the equivalent capacitance $C = C_1 + C_2 = (3 + 6)\;\mu F = 9 \; \mu F$ We have, Energy stored in a capacitor ($C_1$); $E_1 = \frac{1}{2}C\;V^2 = \frac{1}{2} * 3 * 10^{-6} * 300^2 = 0.135\;J$ Energy stored in a capacitor ($C_2$); $E_2 = \frac{1}{2}C\;V^2 = \frac{1}{2} * 6 * 10^{-6} * 300^2 = 0.27\;J$ Energy stored in the equivalence capacitance ($C$); $E = \frac{1}{2}C\;V^2 = \frac{1}{2} * 9 * 10^{-6} * 300^2 = 0.405\;J$ Return to Main Menu

20 Things to know about Relativity

Galileo invented it, Einstein understood it, and Eddington saw it. Credit: vchal/Shutterstock 1. Who invented relativity? Bzzzt - wrong. Galileo hit on the idea in 1639, when he showed that a falling object behaves the same way on a moving ship as it does in a motionless building. 2. And Einstein didn’t call it relativity. The word never appears in his original 1905 paper, “On the Electrodynamics of Moving Bodies,” and he hated the term, preferring “invariance theory” (because the laws of physics look the same to all observers - nothing “relative” about it). 3. Space-time continuum? Nope, that’s not Einstein either. The idea of time as the fourth dimension came from Hermann Minkowski , one of Einstein’s professors, who once called him a “lazy dog.” 4. But Einstein did reformulate Galileo’s relativity to deal with the bizarre things that happen at near-light speed, where time slows down and space gets compressed. That counts for something. 5. Austrian physicist Friedrich Hasenöhrl pub...

Find the half-life of $U^{238}$, if one gram of it emits $1.24 * 10^4$ $\alpha - particles$ per second. (Avogadro's Number = $6.023 * 10^{23}$).

Given, $\frac{dN}{dt}$ $ = 1.24 * 10^{4}$ Half Life $(T_{1/2}) = ?$ But, 238 gm of U contains $6.023 * 10^{23}$ atoms 1 gm of U contains $\frac{6.023 \; * \; 10^{23}}{238}$ $ = 2.51 * 10^{21}$ ⇒ $N = 2.51 * 10^{21}$ atoms We have, $\frac{dN}{dt} = \lambda \; N = \frac{ln(2)}{T_{1/2}} * N$ $T_{1/2} = \frac{0.693 \; * \; N}{\frac{dN}{dt}} = \frac{0.693 \; * \; 2.51 \; * \; 10^{21}}{1.24 \; * \; 10^4}$ $ = 1.41 * 10^{17}\; Sec = 4.5 * 10^9\; years$ Return to Main Menu

Eight drops of water of the same size are equally and similarly charged. They combine together to form a bigger drop. Compare the capacitances of a bigger drop with that of the smaller drop.

Let $r$ be the radius of the smaller drop and $q$ be the charge on it, then charge on bigger drop $Q = 8q$. Now, $R$ be the radius of a bigger drop, then $\frac{4}{3}\; \pi \; R^3 = 8 \; \frac{4}{3} \; \pi \; r^3$ or, $R^3 = 8\;r^3$ ⇒ $R = 2\;r$ ......... (i) Now, Capacitance of bigger drop $C_b = 4\; \pi\; \epsilon_0\; R$ Capacitance of smaller drop $C_s = 4\; \pi\; \epsilon_0\; r$ To compare the capacitance of bigger and smaller drop is, $\frac{C_b}{C_s} = \frac{R}{r} = \frac{2\;r}{r}$ $ = 2$ ∴ $\frac{C_b}{C_s} $ $ = 2$ Return to Main Menu

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