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Delvig [45]
2 years ago
7

A parallel plate capacitor is made of two large plates ofarea

Physics
1 answer:
Murrr4er [49]2 years ago
4 0

Answer:

C = \frac{\epsilon_0 \epsilon_1 A}{\epsilon_0 t + \epsilon_1(a-t)}\\

Explanation:

If there is a dielectric slab with thickness less than the distance between the plates is inserted inside a capacitor, then that capacitor can be regarded as two capacitors connected in series.

Let's assume that the slab is placed onto the lower side. So, the capacitance of that part of the capacitor, C1 is

C_1 = \epsilon_1\frac{A}{t}

where \epsilon_1 is the permittivity of the slab.

The other part of the capacitor is

C_2 = \epsilon_0 \frac{A}{a-t}

Two capacitors are connected in series:

\frac{1}{C} = \frac{1}{C_1} + \frac{1}{C_2} = \frac{1}{\epsilon_1 \frac{A}{t}} + \frac{1}{\epsilon_0 \frac{A}{a-t}} = \frac{t}{\epsilon_1 A} + \frac{a-t}{\epsilon_0 A} = \frac{\epsilon_0 t + \epsilon_1 (a-t)}{\epsilon_0 \epsilon_1 A}\\C = \frac{\epsilon_0 \epsilon_1 A}{\epsilon_0 t + \epsilon_1(a-t)}

If we know the charge of the plates, we could relate the potential V0 to capacitance via

C = \frac{Q}{V_0}

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Solution:

With reference to Fig. 1

Let 'x' be the distance from the wall

Then for \DeltaDAC:

tan\theta = \frac{d}{x}

⇒ \theta = tan^{-1} \frac{d}{x}

Now for the \DeltaBAC:

tan\theta = \frac{d + h}{x}

⇒ \theta = tan^{-1} \frac{d + h}{x}

Now, differentiating w.r.t x:

\frac{d\theta }{dx} = \frac{d}{dx}[tan^{-1} \frac{d + h}{x} -  tan^{-1} \frac{d}{x}]

For maximum angle, \frac{d\theta }{dx} = 0

Now,

0 = [/tex]\frac{d}{dx}[tan^{-1} \frac{d + h}{x} -  tan^{-1} \frac{d}{x}][/tex]

0 = \frac{-(d + h)}{(d + h)^{2} + x^{2}} -\frac{-d}{x^{2} + d^{2}}

\frac{-(d + h)}{(d + h)^{2} + x^{2}} = \frac{{d}{x^{2} + d^{2}}

After solving the above eqn, we get

x = \sqrt{\frac{d}{d + h}}

The observer should stand at a distance equal to x = \sqrt{\frac{d}{d + h}}

4 0
3 years ago
How does sound travel?
Doss [256]

Answer:

Sound vibrations travel in a wave pattern, and we call these vibrations sound waves. Sound waves move by vibrating objects and these objects vibrate other surrounding objects, carrying the sound along. ... Sound can move through the air, water, or solids, as long as there are particles to bounce off of.

Explanation:

8 0
3 years ago
Read 2 more answers
20 POINTS
bekas [8.4K]
They can pretty much be by water i think
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a 5.00 kg plane is speeding up on the ground with an applied force of 706 N. If the net force is 450 N, what would be the force
loris [4]

Answer:

The force due to air resistance is 256 N.

Explanation:

Given;

mass of the plane, m = 5 kg

applied force on the plane, Fa = 706 N

the net force on the plane, ∑F= 450 N

Let the force due to air resistance = Fr

The net force on the plane is given as;

Net force = applied force - force due to air resistance

∑F = Fa - Fr

Fr = Fa - ∑F

Fr = 706 - 450

Fr = 256 N.

Therefore, the force due to air resistance is 256 N.

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