An air-filled parallel-plate capacitor has plates of area 2.30 cm2 2 separated by 1.50 mm. The capacitor is connected to a 12.0-V battery. Find the value of its capacitance.

Answer:

Explanation:

We shall apply the theory of

heat lost = heat gained .

heat lost by water = mass x specific heat x temperature diff

= .285 x 4190 x ( 75.2 - 32 ) = 51587.28 J  

heat gained by ice to attain temperature of zero

= m x 2100 x 22.8 = 47880 m

heat gained by ice in melting = latent heat x mass

= 334000m

heat gained by water at zero to become warm at 32 degree

= m x 4190 x 32 = 134080 m

Total heat gained = 515960 m

So

515960 m = 51587.28

m = .1 kg

= 100 gm

Answer:

5.81 X 10^3 Ns

Explanation:

Given that

F = At² and F at t = 1.25 s is 781.25 N ?

A = F/t² at t = 1.25 s => F = 781.25/(1.25)² = 500 N/s²

d(Impulse) = Fdt

Impulse = ∫Fdt =∫At²dt evaluated in the interval 2.00 s ≤ t ≤ 3.50 s

Impulse = At³/3 = (500/3)(t³) = 166.7t³ between t = 2.00 s and t = 3.50 s

Impulse = 166.7[3.5³ - 2³] = 166.7[42.875 - 8] = 166.7[34.875] = 5813.7 Ns

5.81 X 10^3 N.s

Answer:

C) 200 m/s

Explanation:

The sound travels a total distance of 360 m in 0.03 minutes.

v = (360 m) / (0.03 min × 60 s/min)

v = 200 m/s

Answer:

the correct answer is c     v₁> 12.5 m / s

Explanation:

This is a one-dimensional kinematics exercise, let's start by finding the link to get up to speed.

            v² = v₀² + 2 a₁ x

as part of rest v₀ = 0

           a₁ = v² / 2x

           a₁ = 25² / (2 120)

           a₁ = 2.6 m / s²

now we can find the velocity for the distance x₂ = 60 m

           v₁² = 0 + 2 a1 x₂

           v₁ = Ra (2 2,6 60)

           v₁ = 17.7 m / s

these the speed at 60 m

we see that the correct answer is c     v₁> 12.5 m / s

Answer:

The  angle is  [tex]\theta = 15.48^o[/tex]

Explanation:

From the question we are told that  

     The distance of the dartboard from the dart is  [tex]d = 3.66 \ m[/tex]

     The time taken is  [tex]t = 0.455 \ s[/tex]

The  horizontal component of the speed of the dart is mathematically represented as

      [tex]u_x = ucos \theta[/tex]

where u is the the velocity at dart is lunched

  so

      [tex]distance = velocity \ in \ the\ x-direction * time[/tex]

substituting values

      [tex]3.66 = ucos \theta * (0.455)[/tex]

 =>   [tex]ucos \theta = 8.04 \ m/s[/tex]

From projectile kinematics the time taken by the dart can be mathematically represented as

         [tex]t = \frac{2usin \theta }{g}[/tex]

=>    [tex]usin \theta = \frac{g * t}{2 }[/tex]

       [tex]usin \theta = \frac{9.8 * 0.455}{2 }[/tex]

      [tex]usin \theta = 2.23[/tex]

=>   [tex]tan \theta = \frac{usin\theta }{ucos \theta } = \frac{2.23}{8.04}[/tex]

       [tex]\theta = tan^{-1} [0.277][/tex]

      [tex]\theta = 15.48^o[/tex]

Answer:

122°C

Explanation:

From the data Final temperature is 0 deg C since there is 0.9kg of ice and 1.10kg of liquid water.

That means that 1.10kg of the ice undergoes Heat of Fusion which is 3.34x10^5 J/kg...

Heat lost by copper = Heat gained by ice + Heat of fusion

-> (7.0kg)(390J/kg*C)(0-T) = (2.00kg)(2100J/kg*C)(0 - (-20) + (1.10kg)(3.34x10^5 J/kg)

-> T(2730) = 334001

-> T = 122°C

Answer:

Explanation:

Resistance is defined as the opposition to the flow of an electric current in a circuit. This means that a higher amount of resistance tends to reduce the amount of current flowing through the resistance. The lower the current, the greater the possibility for the resistor to allow current to pass through it.  if a 200 Ω resistor was used in Circuit 1 instead of the 100 Ω resistor, then the current in the circuit will tends to increase since we are replacing the load with a lesser resistor and a smaller resistance tends to allow more current to flow through it

For the potential difference, a decrease in the resistance value will onl decrease the potential difference flowing in the circuit according to ohm's law. According to the law the pd in a circuit is directly proportional to the current which means an increase in the resistance value will cause an increase in the corresponding pd and vice versa.

Answer:

I think answer is zero

bcz momentum=mass×velocity

body was initially at rest it means its velocity is zero

30×0=0

Answer:

d. if any of the above occurs

Explanation:

That is The number of fringes per unit length on the screen can be doubled if

if the distance between the slits is doubled.

if the wavelength is changed to λ = λ/2.

And if the distance between the slits is quadruple the original distance and the wavelength is changed to λ = 2λ

Answer:

Electric field strengh is a measure of the strength of an electric field at a given point in space, equal to the field would induce on a unit electric charge at that point.

Electric field strength is also known as Electric Field Intensity .

Explanation:

Electric Field is also defined as force per charge. The unit will be force unit divided by charge unit. In this case, it will be Newton/Coulomb or N/C.

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Answer:

New location at time 3.01 is given by: (7.49, 2.11)

Explanation:

Let's start by understanding what is the particle's velocity (in component form) in that velocity field at time 3:

[tex]V_x=x^2=7^2=49\\V_y=x+y^2=7+2^2=11[/tex]

With such velocities in the x direction and in the y-direction respectively, we can find the displacement in x and y at a time 0.01 units later by using the formula:

[tex]distance=v\,*\, t[/tex]

[tex]distance_x=49\,(0.01)=0.49\\distance_y=11\,(0.01)=0.11[/tex]

Therefore, adding these displacements in component form to the original particle's position, we get:

New position: (7 + 0.49, 2 + 0.11) = (7.49, 2.11)

Complete question:

A uniform electric field is created by two parallel plates separated by a

distance of 0.04 m. What is the magnitude of the electric field established

between the plates if the potential of the first plate is +40V and the second

one is -40V?

Answer:

The magnitude of the electric field established between the plates is 2,000 V/m

Explanation:

Given;

distance between two parallel plates, d = 0.04 m

potential between first and second plate, = +40V and -40V respectively

The magnitude of the electric field established between the plates is calculated as;

E = ΔV / d

where;

ΔV is change in potential between two parallel plates;

d is the distance between the plates

ΔV = V₁ -V₂

ΔV = 40 - (-40)

ΔV = 40 + 40

ΔV = 80 V

E = ΔV / d

E = 80 / 0.04

E = 2,000 V/m

Therefore, the magnitude of the electric field established between the plates is 2,000 V/m

The magnitude of the electric field developed that lies between the plates should be considered as the 2,000 V/m.

Since

The distance that lies between 2 parallel plates should be d = 0.04 m

The potential that lies between first and second plate should be like +40V and -40V

So, The magnitude of the electric field should be

E = ΔV / d

here,

ΔV represents the change in potential that lies between 2 parallel plates.

d represents the distance between the plates.

So,

ΔV = V₁ -V₂

ΔV = 40 - (-40)

ΔV = 40 + 40

ΔV = 80 V

And,

E = ΔV / d

E = 80 / 0.04

E = 2,000 V/m

Therefore, the magnitude of the electric field established between the plates is 2,000 V/m.

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Answer:

So, according to Einstein's special relativity a person on Mars observe the light to be traveling at c = 3 x 10⁸ m/s.

Explanation:

The special theory of relativity has two main postulates:

1- VALIDITY OF PHYSICAL LAWS

The laws of physics such as Newton's Laws and Maxwell's Equations are valid in all inertial frame of references.

2- CONSTANCY OF SPEED OF LIGHT

The speed of light in vacuum is the same for all observers in uniform translational relative motion, and it is independent of the motion of the source or the observer. Thus, speed of light is a universal constant and its value is c = 3 x 10⁸ m/s.

So, according to Einstein's special relativity a person on Mars observe the light to be traveling at c = 3 x 10⁸ m/s.

Answer:

Explanation:

Using the formula for finding the Z score

Z = x-µ/σ

x is the sample size

µ is the sample mean

σ is the standard deviation

For percentage of the resistors will have resistance between 148 Ω and 152 Ω, or is calculated as shown

P(148≤x152) = Z(152-150/5) - Z(148-150/5)

P(148≤x152) = Z(0.4)-Z( - 0.4)

P(148≤x152) = 0.6554-0.3446

The Z values are from the normal distribution table.

P(148≤x152) = 0.3108

The percentage of resistor that will have between 148 and 152 ohms is 0.3108×100% = 31.08%

Similarly for resistances between 140 Ω and 160 Ω

P(140≤x160) = Z(160-150/5) - Z(140-150/5)

P(140≤x160) = Z(2.0)-Z( - 2.0)

P(140≤x160) = 0.9775-0.02275

The Z values are from the normal distribution table.

P(140≤x160) = 0.9547

The percentage of resistor that will have between 140 and 160ohms is 0.9547×100% = 95.47%

The percentage of the resistors will have resistance between 148 Ω and 152 Ω is 31.08%

The percentage of the resistors will have resistance between 140 Ω and 160 Ω is  95.47%

To solve for the probability we will use the standard score of the Z score, which is given by:

Z = (x - µ)/σ

where x is the sample size

µ is the sample mean = 150Ω

σ is the standard deviation = 5Ω

The probability of the resistors with resistance between 148 Ω and 152 Ω, will be:

P(148 ≤ 152) = Z((152-150)/5) - Z((148-150)/5)

P(148 ≤ 152) = Z(0.4)-Z( - 0.4)

P(148 ≤ 152) = 0.6554-0.3446

P(148 ≤ 152) = 0.3108

So, the percentage will be:

0.3108×100% = 31.08%

Similarly for resistances between 140 Ω and 160 Ω

P(140 ≤ 160) = Z((160-150)/5) - Z((140-150)/5)

P(140 ≤ 160) = Z(2.0)-Z( - 2.0)

P(140 ≤ 160) = 0.9775-0.02275

P(140 ≤ 160) = 0.9547

The percentage of resistor that will have between 140 and 160ohms is 0.9547×100% = 95.47%

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Answer:

Heat transfer is the transmission of heat energy from a body at higher temperature to lower temperature. The three mechanisms of heat transfer are

Example of Conduction:

Heating a metal

Example of Convection:

Sea Breeze

Example of Radiation:

Sun

Hope this helps ;) ❤❤❤

Answer:

Transmission of heat is the movement of thermal energy from one thing to another thing of different temperature.

There are three(3) different ways heat can transfer and they are:

a) Conduction (through direct contact).

b) Convection (through fluid movement).

c) Radiation (through electromagnetic waves).

Examples: 1.Heating a saucepan of water using a coalpot.(conduction&convection).

2. Baking a pie in an oven(radiation).

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Answer:

a) 1764.71 ohms

b) 1.73 H

Explanation:

From the question, we can identify the following parameters;

Vo =12 V , i = 4.86 mA, t =0.700 ms, io =6.80 mA

(a) Indcued emf V = L di/dt =0

From ohms law Vo = ioR

R = 12/6.80*0.001

R=1764.71 ohms

(b) For LR circuit

i =io (1-e^-t/T)

Time constant T = L/R

4.86 = 6.80 (1-e^-0.7*10^-3/T)

divide both side by 6.8

0.715 = 0.0007/T

L/R = 0.0007/0.715

L/R = 0.000979020979

Substitute R from above

L = 0.000979020979 * 1764.71

L =1.73 H

Answer:

Explanation:

Kinetic frictional force acting on the block = μ mg

where μ is coefficient of friction , m is mass of block.

.3 x 1.5 x 9.8 = 4.41 N .

Let v be the velocity of bullet + block after collision

kinetic energy of composite mass after the strike

= 1 /2 x 1.52 x v²

this will be equal to work done by friction .

.76 v² = 4.41 x 7

v² = 40.62

v = 6.37 m /s

Now we can obtain muzzle speed of bullet by applying conservation of momentum .

Let this speed be u

initial momentum of bullet

= .02 x u

final momentum of composite mass

= 1.52 x 6.37

.02 u = 1.52 x 6.37

u = 484.12 m /s .

= 480 m /s ( in two significant figures )

Answer:

A field is a way of mapping forces surrounding any object that can act on another object at a distance without apparent physical connection. The field represents the object generating it. Gravitational fields map gravitational forces, electric fields map electrical forces, and magnetic fields map magnetic forces.

Explanation:

Answer:

    q = q₀ sin (wt)

Explanation:

In your statement it is not clear the type of circuit you are referring to, there are two possibilities.

1) The circuit of this problem is a system formed by an Ac voltage source and a capacitor, in this case all the voltage of the source is equal to the voltage at the terminals of the capacitor

                    ΔV = Δ[tex]V_{C}[/tex]

we assume that the source has a voltage of the form

                    ΔV = ΔV₀o sin wt

The capacitance of a capacitor is

                   C = q / ΔV

                  q = C ΔV sin wt

the current in the circuit is

                    i = dq / dt

                    i = c ΔV₀ w cos wt

if we use

                  cos wt = sin (wt + π / 2)

we make this change by being a resonant oscillation

we substitute

                  i = w C ΔV₀ sin (wt + π/2)

With this answer we see that the current in capacitor has a phase factor of π/2 with respect to the current

2) Another possible circuit is an LC circuit.

In this case the voltage alternates between the inductor and the capacitor

                     V_{L} + V_{C} = 0

                      L di / dt + q / C = 0

the current is

                      i = dq / dt

they ask us for a solution so that

                    L d²q / dt² + 1 / C q = 0

                     d²q / dt² + 1 / LC q = 0

this is a quadratic differential equation with solution of the form

                    q = A sin (wt + Ф)

to find the constant we derive the proposed solution and enter it into the equation

                di / dt = Aw cos (wt + Ф)

                d²i / dt²= - A w² sin (wt + Ф)

                 - A w² + 1 /LC  A = 0

                  w = √ (1 / LC)

To find the phase factor, for this we use the initial conditions for t = 0

in the case of condensate for t = or the charge is zero

                 0 = A sin Ф

                  Ф = 0

                  q = q₀ sin (wt)

Explanation:

Answer:

D. The acceleration vector of the plant points towards the center of the circle. (Works for Apex)

Explanation:

Velocity is always changing because to have velocity you require direction and the direction is always changing when orbiting therefore A and C are not true. And B is not true because the speed of the planet is not accelerating when orbiting around a star.

Complete Question

The  complete question is  shown on the first uploaded image  

Answer:

a

  [tex]f= -75 \ cm = - 0.75 \ m[/tex]

b

  [tex]P = -1.33 \ diopters[/tex]

Explanation:

From the question we are told that

    The  image distance is  [tex]d_i = -75 cm[/tex]

The value of the image is negative because it is on the same side with the corrective glasses

    The  object distance is  [tex]d_o = \infty[/tex]

The  reason object distance  is because the object father than it being picture by the eye

General focal length is mathematically represented as

              [tex]\frac{1}{f} = \frac{1}{d_i} - \frac{1}{d_o}[/tex]

substituting values

             [tex]\frac{1}{f} = \frac{1}{-75} - \frac{1}{\infty}[/tex]

=>         [tex]f= -75 \ cm = - 0.75 \ m[/tex]

Generally the power of the corrective lens is  mathematically represented as

        [tex]P = \frac{1}{f}[/tex]

substituting values

       [tex]P = \frac{1}{-0.75}[/tex]

        [tex]P = -1.33 \ diopters[/tex]

5.19 x 10³Hz

The capacitive reactance, [tex]X_{C}[/tex], which is the opposition given to the flow of current through the capacitor is given by;

[tex]X_C = \frac{1}{2\pi fC }[/tex]

Where;

f = frequency of the signal through the capacitor

C = capacitance of the capacitor.

Also, from Ohm's law, the voltage(V) across the capacitor is given by the product of current(I) and the capacitive reactance. i.e;

V = I x [tex]X_{C}[/tex]             [Substitute the value of

=> V = I x [tex]\frac{1}{2\pi fC}[/tex]      [Make f the subject of the formula]

=> f = [tex]\frac{I}{2\pi VC}[/tex]                    ---------------------(i)

From the question;

I = 3.33mA = 0.00333A

C = 8.50nF = 8.50 x 10⁻⁹F

V = 12.0V

Substitute these values into equation (i) as follows;

f = [tex]\frac{0.00333}{2 * 3.142 * 12.0 * 8.50 * 10^{-9}}[/tex]            [Taking [tex]\pi[/tex] = 3.142]

f = 5.19 x 10³Hz

Therefore, the frequency is closest to f = 5.19 x 10³Hz

Answer:

Peak current= 84.86 A

Area of each turn = 0.029 m^2

Explanation:

The peak value of current can be obtained from Irms= 0.707Io. Where Io is the peak current.

Hence;

Irms= 60.0A

Io= Irms/0.707

Io = 60.0/0.707

Io= 84.86 A

Vrms= 0.707Vo

Vo= Vrms/0.707= 170/0.707 = 240.45 V

From;

V0 = NABω

Where;

Vo= peak voltage

N= number of turns

B= magnetic field

A= area of each coil

ω= angular velocity

But ω= 2πf = 2×π×95= 596.9 rads-1

Substituting values;

A= Vo/NBω

A= 240.45/550×0.025×596.9

A= 0.029 m^2

Answer:

a)

6t i + t² j m

b)

6 i + 2 t j m/s

c)

x = 24 m and y = 16 m

d)

10 m/s

Explanation:

Explanation is given in the attached document.

Answer:

The flow rate is  [tex]R =2.357 *10^{-4} \ m^3/s[/tex]

Explanation:

From the question we are told that

    The velocity is [tex]v = 3.0 \ m/s[/tex]

   The  diameter of the pipe is  [tex]d = 1.0 \ cm = 0.01 \ m[/tex]

The  radius of the pipe is mathematically represented as

            [tex]r = \frac{d}{2}[/tex]

substituting values

            [tex]r = \frac{0.01}{2}[/tex]

           [tex]r = 0.005 \ m[/tex]

The flow rate is mathematically represented as

       [tex]R = v * A[/tex]

Where is the cross-sectional area of the pipe which is mathematically evaluated as

      [tex]A = \pi r^2[/tex]

substituting values

      [tex]A = 3.142 * (0.005)^2[/tex]

     [tex]A = 7.855 * 10^{-5} \ m^2[/tex]

So

    [tex]R = 3.0 * 7.855 *10^{-5}[/tex]

    [tex]R = 2.357*10^{-4} \ m^3 /s[/tex]

Answer:

To reverse the direction of an electric current, we simply reverse the voltage either automatically with the help of some switching circuitry or manually by changing the voltage source terminals connection.  

Explanation:

For electric current to flow, there must be a potential difference, usually referred to as the voltage. The electric current flow is analogous to the flow of water under the action of a pump, through a series of pipe connections. The voltage is similar to the driving action of the pump, and current flows the same way water flows. The resistance due to drag on the pipe wall is equivalent to electric resistance. For current to flow in the reverse direction, the voltage or rather, the potential difference is changed, causing the current to flow in the opposite direction. This can be done by switching the terminals of the voltage source, or by automatic means. The automatic switching can be done with a transistor based circuitry.

Answer:

Each of the capacitor carries the same charge, Q

Explanation:

When capacitors are connected in series, the battery voltage is divided equally across the capacitors. The total voltage across the three identical capacitors is calculated as follows;

[tex]V_T = V_1 + V_2 + V_3[/tex]

We can also calculate this voltage in terms of capacitance and charge;

[tex]V = \frac{Q}{C} \\\\V_T = V_1 + V_2 +V_3 \\\\(given \ total \ charge \ as \ Q, then \ the \ total \ voltage \ V_T \ can \ be \ written \ as)\\\\V_T = \frac{Q}{C_1} + \frac{Q}{C_2} + \frac{Q}{C_3} \\\\V_T = Q(\frac{1}{C_1 } +\frac{1}{C_2} + \frac{1}{C_3 })\\\\[/tex]

Therefore, each of the capacitor carries the same charge, Q

Answer:

The mass of the fluid is 72 g.

Explanation:

The following data were obtained from the question:

Height (h) = 10 cm

Area of cross section (A) = 36cm²

Relative density = 0.2

Mass =..?

Next, we shall determine the volume of the cylinder. This can be achieved by doing the following:

Volume = Area x Height

Volume = 36 x 10

Volume = 360 cm³

Next, we shall determine the density of the liquid.

This can be obtained as follow:

Relative density = density of substance/density of water.

Relative density = 0.2

Density of water = 1 g/cm³

Density of fluid =...?

Relative density = density of substance/density of water.

0.2 = density of fluid / 1 g/cm³

Cross multiply

Density of fluid = 0.2 x 1 g/cm³

Density of fluid = 0.2 g/cm³

Finally, we shall determine the mass of fluid as follow:

Volume = 360 cm³

Density of fluid = 0.2 g/cm³

Mass of fluid =...?

Density = mass /volume.

0.2 g/cm³ = mass of fluid /360 cm³

Cross multiply

Mass of fluid = 0.2 g/cm³ x 360 cm³

Mass of fluid = 72 g

Therefore, the mass of the fluid in the jar is 72 g.

Answer:

V2 = 21.44cm^3

Explanation:

Given that: the initial volume of the bubble = 1.3 cm^3

Depth = h = 160m

Where P2 is the atmospheric pressure = Patm

P1 is the pressure at depth 'h'

Density of water = ρ = 10^3kg/m^3

Patm = 1.013×10^5 Pa.

Patm = 101300Pa

g = 9.81m/s^2

P1 = P2+ρgh

P1 = Patm +ρgh

P1 = 1.013×10^5+10^3×9.81×160.

P1 = 101300+1569600

P1 = 1670900 Pa

For an ideal gas law

PV =nRT

P1V1/P2V2 = 1

V2 = ( P1/P2)V1

V2 = (P1/Patm)V1

V2 = ( 1670900 /101300 Pa) × 1.3

V2 = 1670900/101300

V2 = 16.494×1.3

V2 = 21.44cm^3

The volume of the bubble can be determined using ideal gas law. The volume of the bubble when it reaches surface is 21.44 [tex]\bold {cm^3}[/tex].

The formula of the pressure of the static fluid

P1 = P2+ρgh

Where,

P1 -  pressure at depth 'h'

P2 -  atmospheric pressure = [tex]\bold {1.013x10^5 }[/tex] =  1670900 Pa

h - Depth = 160m  

ρ - Density of water = [tex]\bold {10^3\ kg/m^3}[/tex]

g- gravitational acceleration = [tex]\bold {9.81\ m/s^2}[/tex]

The initial volume of the bubble = [tex]\bold {1.3\ cm^3}[/tex]  

[tex]\bold {P1 = 1.013x10^5+10^3\times 9.81\times 160}\\\\\bold {P1 = 101300+1569600}\\\\\bold {P1 = 1670900\ Pa}[/tex]  

 For an ideal gas,  

PV =nRT  

[tex]\bold {\dfrac {P_1V_1}{P_2V_2 }= 1}[/tex]  

[tex]\bold {V2 = \dfrac { P_1}{P_2V_1}}[/tex]

So,

[tex]\bold {V2 = \dfrac {1670900 }{101300 }\times 1.3}\\\\\bold {V2 =21.44\ cm^3}[/tex]  

Therefore, the volume of the bubble when it reaches surface is 21.44 [tex]\bold {cm^3}[/tex].

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Answer:

a= 4.9m/s²

Explanation:

Using Fnet= mgsintheta = ma

But a= gsintheta

a= 9.8xsin 30

= 4.9m/s²