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erica [24]
3 years ago
10

A parallel plates capacitor is filled with a dielectric of relative permittivity ε = 12 and a conductivity σ = 10^-10 S/m. The c

apacitor is fully charged at a voltage V=10V and then disconnected from the battery. Find the time after wich the voltage in the capacitor decays to 3.67 V?
Engineering
1 answer:
monitta3 years ago
3 0

Answer:

t = 1.06 sec

Explanation:

Once disconnected from the battery, the capacitor discharges through the internal resistance of the dielectric, which can be expressed as follows:

R = (1/σ)*d/A, where d is is the separation between plates, and A is the area of one of  the plates.

The capacitance C , for a parallel plates capacitor filled with a dielectric of a relative permittivity ε, can be expressed in this way:

C = ε₀*ε*A/d = 8.85*10⁻¹² *12*A/d

The voltage in the capacitor (which is proportional to the residual charge as it discharges through the resistance of the dielectric) follows an exponential decay, as follows:

V = V₀*e(-t/RC)

The product RC (which is called the time constant of the circuit) can be calculated as follows:

R*C = (1/10⁻¹⁰)*d/A*8.85*10⁻¹² *12*A/d

Simplifying common terms, we finally have:

R*C = 8.85*10⁻¹² *12 / (1/10⁻¹⁰) sec = 1.06 sec

If we want to know the time at which the voltage will decay to 3.67 V, we can write the following expression:

V= V₀*e(-t/RC) ⇒ e(-t/RC) = 3.67/10 ⇒ -t/RC = ln(3.67/10)= -1

⇒ t = RC = 1.06 sec.

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Answer:

V = 0.30787 m³/s

m = 2.6963 kg/s

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Explanation:

given data

diameter = 28 cm

steadily =200 kPa

temperature = 20°C

velocity = 5 m/s

solution

we know mass flow rate is

m = ρ A v

floe rate V = Av

m = ρ V

flow rate = V = \frac{m}{\rho}

V = Av = \frac{\pi}{4} * d^2 * v1

V = \frac{\pi}{4} * 0.28^2 * 5

V = 0.30787 m³/s

and

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m = ρ A v

m = ρ V

m = \frac{V}{v} = \frac{0.30787}{0.11418}

m = 2.6963 kg/s

and

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velocity = mass × v

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and

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v2 = \frac{0.3705}{\frac{\pi}{4} * 0.28^2}

v2 = 6.017 m/s

7 0
3 years ago
The cube measures 3.0-ft on all sides and has a density of 3.1 slugs/ft3. How much does it weigh?
kodGreya [7K]

Answer:

W = 2695.14 lb

Explanation:

given,

side of cube = 3 ft

density of the cube = 3.1 slugs/ft³

we know,

density = \dfrac{mass}{volume}

mass = density x volume

volume = 3³ = 27 ft³

mass =  3.1  x 27

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weight calculation

converting mass from slug to pound

weight of 1 slug is equal to 32.2 lb

now,

weight of the cube is equal to

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yanalaym [24]

Answer: Electric current originates from positively charged protons negatively charged electrons of an atom.

Explanation:

The movement of ions (positive or negative) from one point to another is called electric current.

An atom has three sub-atomic particles. These are protons, neutrons and electrons.

Protons are positively charged, neutrons have no charge and electrons are negatively charged. Protons and neutrons reside inside the nucleus of an atom whereas electrons revolve around the nucleus.

So, protons and electrons are responsible for originating electric current form an atom as these are the charged particles.

Thus, we can conclude that electric current originates from positively charged protons negatively charged electrons of an atom.

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