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LUCKY_DIMON [66]
3 years ago
8

The terminals of a 1.30 mF parallel-plate vacuum capacitor is connected to a battery that keeps a voltage of 29.6 V across the p

lates. Then, without disconnecting the battery, a piece of material with dielectric constant of 3.51 is inserted between the plates. After inserting the dielectric, how much energy (in Joules) is stored in the capacitor?

Physics
2 answers:
lapo4ka [179]3 years ago
3 0

Answer:

The energy stored in the capacitor after replacing the dielectric material = 2.00 J

Explanation:

The energy stored in a capacitor is given by

E = ½CV²

where C = capacitance of the capacitor; initially with vacuum as dielectric material is equal to 1.30 mF

V = voltage across the capacitor = 29.6 V

The capacitance of a capacitor is also given as

C = (Aε/d)

A = Cross sectional Area of the capacitor

d = distance between the plates of the capacitor

ε = permissivity of material between the plates of the capacitor

ε = kε₀

k = relative permissivity

ε₀ permissivity of vacuum.

If the Cross sectional Area of the capacitor and the distance between the plates of the capacitor are constant, it is evident that the capacitance of the capacitor is directly proportional to the permissivity of the dielectric material.

C₀ = (Aε₀/d) = 1.30 mF

C = (Aε/d) = (kAε₀/d) = kC₀

For the is question, the relative permissivity = 3.51

C = 3.51 × 1.30 mF = 4.563 mF = 0.004563 F

Energy stored in a capacitor is still

E = ½CV²

C = 4.563 mF = 0.004563 F

V = 29.6 V

E = (1/2)(0.004563)(29.6²)

E = 1.99895904 J = 2.00 J

Hope this Helps!!!

Ludmilka [50]3 years ago
3 0

Answer:

Energy stored in capacitor with new dielectric is 1.998 joules approximately 2 joules

Explanation:

Detailed explanation and calculation is shown in the image

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A 44-cm-diameter water tank is filled with 35 cm of water. A 3.0-mm-diameter spigot at the very bottom of the tank is opened and
cricket20 [7]

Answer:

The frequency f = 521.59 Hz

The rate at which the frequency is changing = 186.9 Hz/s

Explanation:

Given that :

Diameter of the tank = 44 cm

Radius of the tank = \frac{d}{2} =\frac{44}{2} = 22 cm

Diameter of the spigot = 3.0 mm

Radius of the spigot = \frac{d}{2} =\frac{3.0}{2} = 1.5 mm

Diameter of the cylinder = 2.0 cm

Radius of the cylinder = \frac{d}{2} = \frac{2.0}{2} = 1.0 cm

Height of the cylinder = 40 cm = 0.40 m

The height of the water in the tank from the spigot = 35 cm = 0.35 m

Velocity at the top of the tank = 0 m/s

From the question given, we need to consider that  the question talks about movement of fluid through an open-closed pipe; as such it obeys Bernoulli's Equation and the constant discharge condition.

The expression for Bernoulli's Equation is as follows:

P_1+\frac{1}{2}pv_1^2+pgy_1=P_2+\frac{1}{2}pv^2_2+pgy_2

pgy_1=\frac{1}{2}pv^2_2 +pgy_2

v_2=\sqrt{2g(y_1-y_2)}

where;

P₁ and P₂ = initial and final pressure.

v₁ and v₂ = initial and final fluid velocity

y₁ and y₂ = initial and final height

p = density

g = acceleration due to gravity

So, from our given parameters; let's replace

v₁ = 0 m/s ; y₁ = 0.35 m ; y₂ = 0 m ; g = 9.8 m/s²

∴ we have:

v₂ = \sqrt{2*9.8*(0.35-0)}

v₂ = \sqrt {6.86}

v₂ = 2.61916

v₂ ≅ 2.62 m/s

Similarly, using the expression of the continuity for water flowing through the spigot into the cylinder; we have:

v₂A₂ = v₃A₃

v₂r₂² = v₃r₃²

where;

v₂r₂ = velocity of the fluid and radius at the spigot

v₃r₃ = velocity of the fluid and radius at the cylinder

v_3 = \frac{v_2r_2^2}{v_3^2}

where;

v₂ = 2.62 m/s

r₂ = 1.5 mm

r₃ = 1.0 cm

we have;

v₃ = (2.62  m/s)* (\frac{1.5mm^2}{1.0mm^2} )

v₃ = 0.0589 m/s

∴ velocity  of the fluid in the cylinder =  0.0589 m/s

So, in an open-closed system we are dealing with; the frequency can be calculated by using the expression;

f=\frac{v_s}{4(h-v_3t)}

where;

v_s = velocity of sound

h = height of the fluid

v₃ = velocity  of the fluid in the cylinder

f=\frac{343}{4(0.40-(0.0589)(0.4)}

f= \frac{343}{0.6576}

f = 521.59 Hz

∴ The frequency f = 521.59 Hz

b)

What are the rate at which the frequency is changing (Hz/s) when the cylinder has been filling for 4.0 s?

The rate at which the frequency is changing is related to the function of time (t) and as such:

\frac{df}{dt}= \frac{d}{dt}(\frac{v_s}{4}(h-v_3t)^{-1})

\frac{df}{dt}= -\frac{v_s}{4}(h-v_3t)^2(-v_3)

\frac{df}{dt}= \frac{v_sv_3}{4(h-v_3t)^2}

where;

v_s (velocity of sound) = 343 m/s

v₃ (velocity  of the fluid in the cylinder) = 0.0589 m/s

h (height of the cylinder) = 0.40 m

t (time) = 4.0 s

Substituting our values; we have ;

\frac{df}{dt}= \frac{343*0.0589}{4(0.4-(0.0589*4.0))^2}

= 186.873

≅ 186.9 Hz/s

∴ The rate at which the frequency is changing = 186.9 Hz/s  when the cylinder has been filling for 4.0 s.

8 0
3 years ago
What are the differences between refraction and diffraction?
Liula [17]
Refraction is the change in direction of a wave.
Diffraction is the bending of a wave around a barrier.
5 0
3 years ago
A sample of radium-226 will decay to ¼ of its original amount after 3200 years. What is the half-life of radium-226?
lesantik [10]
<h3><u>Answer</u>;</h3>

1600 years

<h3><u>Explanation</u>;</h3>
  • Half life is the time taken for a radioactive isotope to decay by half of its original amount.
  • We can use the formula; N = O × (1/2)^n ; where N is the new mass, O is the original amount and n is the number of half lives.
  • A sample of radium-226 takes 3200 years to decay to 1/4 of its original amount.

Therefore;

<em>1/4 = 1 × (1/2)^n</em>

<em>1/4 = (1/2)^n </em>

<em>n = 2 </em>

Thus; <em>3200 years is equivalent to 2 half lives.</em>

<em>Hence, the half life of radium-226 is 1600 years</em>

3 0
3 years ago
Pls help me I don’t get it :(
Ksju [112]

Answer:

2nd and 4th

Explanation:

4 0
3 years ago
How do i find stretch? The problem in questioning has already given me the elastic energy and k-value, but I have no idea how to
finlep [7]

Answer:

Stretch can be obtained using the Elastic potential energy formula.

The expression to find the stretch (x) is x=\sqrt{\frac{2\times EPE}{k}}

Explanation:

Given:

Elastic potential energy (EPE) of the spring mass system and the spring constant (k) are given.

To find: Elongation in the spring (x).

We can find the elongation or stretch of the spring using the formula for Elastic Potential Energy (EPE).

The formula to find EPE is given as:

EPE=\frac{1}{2}kx^2

Rewriting the above expression in terms of 'x', we get:

x=\sqrt{\frac{2\times EPE}{k}}

Example:

If EPE = 100 J and spring constant, k = 2 N/m.

Elongation or stretch is given as:

x=\sqrt{\frac{2\times EPE}{k}}\\\\x=\sqrt{\frac{2\times 100}{2}}\\\\x=\sqrt{100}=10\ m

Therefore, the stretch in the spring is 10 m.

So, stretch in the spring can be calculated using the formula for Elastic Potential Energy.

6 0
3 years ago
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