Answer:
C = 2.9 10⁻⁵ F = 29 μF
Explanation:
In this exercise we must use that the voltage is
V = i X
i = V/X
where X is the impedance of the system
in this case they ask us to treat the system as an RLC circuit in this case therefore the impedance is
X =
tells us to take inductance L = 0.
The angular velocity is
w = 2π f
the current is required to be half the current at high frequency.
Let's analyze the situation at high frequency (high angular velocity) the capacitive impedance is very small
→0 when w → ∞
therefore in this frequency regime
X₀ = ![\sqrt{R^2 + ( \frac{1}{2\pi 2 10^4 C} )^2 } = R \sqrt{ 1+ \frac{8 \ 10^{-10} }{RC} }](https://tex.z-dn.net/?f=%5Csqrt%7BR%5E2%20%2B%20%28%20%5Cfrac%7B1%7D%7B2%5Cpi%20%202%2010%5E4%20C%7D%20%29%5E2%20%7D%20%3D%20%20R%20%20%5Csqrt%7B%201%2B%20%5Cfrac%7B8%20%5C%2010%5E%7B-10%7D%20%7D%7BRC%7D%20%20%20%20%20%7D)
the very small fraction for which we can despise it
X₀ = R
to halve the current at f = 200 H, from equation 1 we obtain
X = 2X₀
let's write the two equations of inductance
X₀ = R w → ∞
X= 2X₀ =
w = 2π 200
we solve the system
2R = \sqrt{R^2 +( \frac{1}{wC} )^2 }
4 R² = R² + 1 / (wC) ²
1 / (wC) ² = 3 R²
w C =
C =
let's calculate
C =
C = 2.9 10⁻⁵ F
C = 29 μF
The answer is Circulatory System
It depends how the sound travels and the conditions, The speed of sound in dry air, 20°C is 323 m/s
What a delightful little problem !
Here's how I see it:
When 'C' is touched to 'A', charge flows to 'C' until the two of them are equally charged. So now, 'A' has half of its original charge, and 'C' has the other half.
Then, when 'C' is touched to 'B', charge flows to it until the two of <u>them</u> are equally charged. How much is that ? Well, just before they touch, 'C' has half of an original charge, and 'B' has a full one, so 1/4 of an original charge flows from 'B' to 'C', and then each of them has 3/4 of an original charge.
To review what we have now: 'A' has 1/2 of its original charge, and 'B' has 3/4 of it.
The force between any two charges is:
F = (a constant) x (one charge) x (the other one) / (the distance between them)².
For 'A' and 'B', the distance doesn't change, so we can leave that out of our formula.
The original force between them was 3 = (some constant) x (1 charge) x (1 charge).
The new force between them is F = (the same constant) x (1/2) x (3/4) .
Divide the first equation by the second one, and you have a proportion:
3 / F = 1 / ( 1/2 x 3/4 )
Cross-multiply this proportion:
3 (1/2 x 3/4) = F
F = 3/2 x 3/4 = 9/8 = <em>1.125 newton</em>.
That's my story, and I'm sticking to it.