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blondinia [14]
3 years ago
15

In an RC-circuit, a resistance of R=1.0 "Giga Ohms" is connected to an air-filled circular-parallel-plate capacitor of diameter

12.0 mm with a separation distance of 1.0 mm. What is the time constant of the system?
Physics
1 answer:
solniwko [45]3 years ago
7 0

Answer:

\tau = 1\ ms

Explanation:

First we need to find the capacitance of the capacitor.

The capacitance is given by:

C = \epsilon_0 * area / distance

Where \epsilon_0 is the air permittivity, which is approximately 8.85 * 10^(-12)

The radius is 12/2 = 6 mm = 0.006 m, so the area of the capacitor is:

Area = \pi * radius^{2}\\Area = \pi * 0.006^2\\Area = 113.1 * 10^{-6}\ m^2

So the capacitance is:

C = \frac{8.85 * 10^{-12} * 113.1 * 10^{-6}}{0.001}

C = 10^{-12}\ F = 1\ pF

The time constant of a rc-circuit is given by:

\tau = RC

So we have that:

\tau = 10^{9} * 10^{-12} = 10^{-3}\ s = 1\ ms

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1. If an object of mass m collides and velocity v collides inelastically with an object of mass 3m that is initially at rest, th
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1a). 4 times. 1b) 4. 1c) 1/4.

2a) 5 times. 1b) 5 1c) 1/5

3a) 7/3 times 3b) 7/3 3c) 3/7

4a) 8/5 times 4b) 8/5 4c) 5/8

Explanation:

1) Assuming no external forces acting during the collision, total momentum must be conserved, so the following general expression applies:

m₁*v₁₀ + m₂*v₂₀ = m₁*v₁f  + m₂*v₂f (1)

If we assume that the collision is perfectly inelastic, this means that both masses stick together after the collision, so v₁f = v₂f.

If m₂ is initially at rest, ⇒ v₂₀ = 0.

Replacing in (1) we get the expression of vf as a function of v₁₀, as follows:

vf = v₁₀*(m₁/(m₁+m₂)

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1) initial mass = m

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⇒final mass / initial mass = 4

vf = v₀* (m/4m) = v₀/4  ⇒v₀/vf = 4

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2a)  final mass / initial mass = 5

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2c) vf = v₀/5

3) Applying the same considerations, we get:

3a)  final mass / initial mass = 7/3

3b) vf = v₀* (3m/7m) =3/7* v₀  ⇒v₀/vf = 7/3

3c) vf = 3/7*v₀

4) Applying the same considerations, we get:

4a)  final mass / initial mass = 8/5

4b) vf = v₀* (5m/8m) = 5/8*v₀ ⇒v₀/vf = 8/5

4c) vf = 5/8*v₀

3 0
3 years ago
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