Answer:
the tension in the cable is [tex]\mathbf{F = \frac{\pi E_o v^2r^2}{2d^2}}[/tex]
the work done by the cable is [tex]\mathbf{W= \frac{\pi E_ov^2r^2}{4d}}[/tex]
Explanation:
A)
If we have two circular plate supported by a cable at a fixed distance, then the electric field formed between the two plate of the capacitor can be represented by the equation.
[tex]\mathbf{E = \frac{voltage \ \ V}{distance \ \ d}}[/tex]
However; the net electric field i.e the sum of the electric filed produced is represented as:
[tex]\mathbf{E' = \frac{E}{2}} \\ \\ \mathbf{E' = \frac{V}{2d}}[/tex]
So, if we assume that the lower plate and the upper plate possess the charge +q and -q respectively. Then, the tension of the cable which is the same as Force F can be written as:
[tex]\mathbf{F = q* E'}[/tex]
[tex]\mathbf{F = \frac{q*v}{2d}}[/tex] ----- equation (1)
Also ; we know that
[tex]\mathbf{C = \frac{q}{v}= \frac{E_oA}{d}}[/tex]
[tex]\mathbf{\frac{q}{v}= \frac{E_o \pi r^2}{d}} \ \ \ \ \ \mathbf{since \ A = \pi r^2}[/tex]
[tex]\mathbf{{q}= \frac{\pi E_o {v} r^2}{d}}[/tex] ----- equation (2)
Replacing equation 3 into equation (2); we have:
[tex]\mathbf{F = \frac{\pi E_o vr^2}{d}* \frac{v}{2d}}[/tex]
[tex]\mathbf{F = \frac{\pi E_o v^2r^2}{2d^2}}[/tex]
Therefore, the tension in the cable is [tex]\mathbf{F = \frac{\pi E_o v^2r^2}{2d^2}}[/tex]
B)
Assume that the upper plate is displaced by dz in an upward direction ; Then we can express the workdone by the tension as :
[tex]\mathbf{dW = T *dz} \\ \\ \mathbf{dW = F*dz} \\ \\ \mathbf{dW = \frac{\pi E_o v^2r^2}{2z^2}dz }[/tex]
The net workdone to raise the plate from separation d to 2d is:
[tex]\mathbf{W = \int\limits^{2d}_{2zd} {dw} = \frac{\pi E_ov^2r^2}{2} \int\limits^{2d}_d \frac{dz}{z^2} }[/tex]
[tex]\mathbf{W= \frac{\pi E_ov^2r^2}{2} [-\frac{1}{z}]^{2d}_d }[/tex]
[tex]\mathbf{W= - \frac{\pi E_ov^2r^2}{2} [\frac{1}{2d}-\frac{1}{d}]}[/tex]
[tex]\mathbf{W= - \frac{\pi E_ov^2r^2}{2} [\frac{-1}{2d}]}[/tex]
[tex]\mathbf{W= \frac{\pi E_ov^2r^2}{4d}}[/tex]
the work done by the cable is [tex]\mathbf{W= \frac{\pi E_ov^2r^2}{4d}}[/tex]
C) To calculate the energy stored in the Electrical energy Capacitor before the top plate is raised ; we have:
[tex]\mathbf{U_i = \frac{1}{2}Cv^2} \\ \\ \mathbf{U_i = \frac{1}{2}(\frac{E_oA}{d})v^2} \\ \\ \mathbf{U_i = \frac{1}{2}(\frac{E_o \pi r^2}{d})v^2} \\ \\ \mathbf{U_i = \frac{E_o \pi r^2 v^2}{2d}} }[/tex]
D) The energy stored in the plate after the the top plate was raised is as follows:
[tex]\mathbf{U_f = \frac{1}{2}C'v^2} \\ \\ \mathbf{U_f = \frac{1}{2}(\frac{E_oA}{2d})v^2} \\ \\ \mathbf{U_f = \frac{1}{2}(\frac{E_o \pi r^2}{2d})v^2} \\ \\ \mathbf{U_f = \frac{E_o \pi r^2 v^2}{4d}} }[/tex]
E) Yes, work done by the cable equal to the change in the stored electrical energy. The Difference in energy stored before and after the top plate is raised:
[tex]\mathbf{U_i-U_f} = \mathbf{\frac{E_o \pi r^2 v^2}{2d}} }} - \mathbf {\frac{E_o \pi r^2 v^2}{4d}} }}[/tex]
[tex]\mathbf{U_i-U_f}= \mathbf {\frac{E_o \pi r^2 v^2}{4d}} }}[/tex]
Thus;
b)The work done in separating the plates is equal to the magnitude of the energy change in the plates. This does not mean that the work done is equal to the change in the energy stored in the plates.
who is the first person created light bulb
Answer:
Thomas Alva EdisonExplanation:
he created the bulb first. He was an American. He was an inventor and also a businessman. Moreover he invented the phonograph, and the motion picture camera, as well as improving the telegraph and telephone.
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What is a neutral subatomic particle that has almost no mass and is released
from a radioactive nucleus during by fission and fusion reactions. These particles
can usually pass through matter undetected.
Answer:
Alpha particle
Explanation:
Alpha particles emitted by radioactive nuclei consist of 2 protons and 2 neutrons bound together which makes it neutral and are able to pass through ordinary matter almost undisturbed
Ned tightens a bolt in his car engine by exerting 15 N of force on his wrench at a distance of 0.45m from the fulcrum. How much torque must Ned produce to turn the bolt?
Answer:
[tex]T = 6.75\,N\cdot m[/tex]
Explanation:
Vectorially speaking, torque is the cross product between force and distance from fulcrum. Its magnitude is equal to the following expression:
[tex]T = F\cdot r \cdot \sin \theta[/tex]
[tex]T = F_{\bot} \cdot r[/tex]
Let assume that force is perpendicular to the distance from the fulcrum. So, the torque needed to turn the bolt is:
[tex]T = (15\,N)\cdot (0.45\,m)[/tex]
[tex]T = 6.75\,N\cdot m[/tex]
ellus
Three horizontal forces are pulling on a
ring, at rest. F1 is 12.0 N at a 0° angle, and
F2 is 18.0 N at a 90° direction. What is the
x-component of F3?
Answer:
Explanation:
Three forces are in equilibrium .
Let us represent forces in vector form ie in the form of i and j .
F₁ is acting along positive x axis ( at a 0° angle )
F₁ = 12 i
F₂ is acting along positive y axis ( at a 90° direction)
F₂ = 18 j
Suppose F₃ is represented by X i + Y j
Total of three forces is zero .
F₁ + F₂ + F₃ = 0
12 i + 18 j + F₃ = 0
F₃ = - 12i - 18 j
So x - component of F₃ = - 12 i
X - component of F₃ is equal to 12 N in magnitude and is acting in negative x direction ie at 180° direction .
similarly y - component is 18 N acting in negative y direction.
Answer:
x-component: -12
y-component- -18
Explanation:
A mass weighting 48 lbs stretches a spring 6 inches. The mass is in a medium that exerts a viscous resistance of 27 lbs when the mass has a velocity of 6 ft/sec. Suppose the object is displaced an additional 6 inches and released.
Required:
a. Find an equation for the object's displacement, u(t), in feet after t seconds.
b. What is the mass of the object?
c. What is the damping coefficient?
d. What is the spring constant?
Answer:
a)
[tex]u(t)=0.499ft.e^{-\frac{144.76lb/s}{2(48lb)}t}cos(\omega t)\\\\u(t)=0.499ft.e^{-1.5t}cos(\omega t)[/tex]
b)
m = 48lb
c)
b = 144.76lb
Explanation:
The general equation of a damping oscillate motion is given by:
[tex]u(t)=u_oe^{-\frac{b}{2m}t}cos(\omega t-\alpha)[/tex] (1)
uo: initial position
m: mass of the block
b: damping coefficient
w: angular frequency
α: initial phase
a. With the information given in the statement you replace the values of the parameters in (1). But first, you calculate the constant b by using the information about the viscous resistance force:
[tex]|F_{vis}|=bv\\\\b=\frac{|F_{vis}|}{v}\\\\|F_{vis}|=27lbs=27*32.17ft.lb/s^2=868.59ft.lb/s^2\\\\b=\frac{868.59}{6}lb/s=144.76lb/s[/tex]
Then, you obtain by replacing in (1):
6in = 0.499 ft
[tex]u(t)=0.499ft.e^{-\frac{144.76lb/s}{2(48lb)}t}cos(\omega t)\\\\u(t)=0.499ft.e^{-1.5t}cos(\omega t)[/tex]
b.
mass, m = 48lb
c.
b = 144.76 lb/s
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An elevator with a person inside weighs a total of 24,450 Newtons. an elevator that rises 12 meters in 30 seconds. How much power is needed for the elevator trip?
Answer:
9780 W
Explanation:
Power: This can be defined as the rate at which work is done. The S.I unit of power is Watt (W).
From the question,
P = W/t....................... Equation 1
Where P = power, W = work, t = time.
But,
W = F×d.............. Equation 2
Where F = force, d = distance.
Substitute equation 2 into equation 1
P = (F×d)/t................. Equation 3
Given: F = 24450 N, d = 12 m, t = 30 s.
Substitute these vales into equation 3
P = (24450×12)/30
P = 9780 W.
Hence the power needed for the elevator trip = 9780 W
Answer:
9,780WattsExplanation:
Power is defined as the rate of workdone with respect to time.
The formula for calculating power P needed by the eleveator is expressed as;
Power = [tex]\frac{workdone}{time}[/tex]
Since Workdone = Force*distance then;
[tex]Power = \frac{force * distance}{time}[/tex]
Given the weight of elevator = 24,450Newtons
distance moved by the elevator = 12m
time taken = 12seconds.
Substituting this values in the formula given will give;
[tex]Power = \frac{24,450*12}{30} \\Power = \frac{293,400}{30} \\Power = 9,780Watts\ or\ 9.78kW[/tex]
The amount of power needed for the elevator trip is 9,780Watts
2. Water at the Antarctica usually exits as ice, making it very difficult to use the water or conduct experiment requiring the water to be in liquid state. A coffee addicted physicist stationed at a research base requires about 0.8 kg of ice for his coffee on the hour.
a. How much heat is required to convert 0.8 kg of ice at —35 °C into steam at 100°C?
Answer:
662480 J
Explanation:
The heat required to convert 0.8Kg of ice at -35°c to steam at 100°c is the sum of the heat required to raise the temperature of the ice from -35°c to 0°C, the latent heat of fusion of ice and the heat required to raise the temperature of the ice from 0°c to 100°c.
Latent heat of fusion for ice= 3.36× 10^5 J Kg-1
Specific heat capacity of ice= 2060 J kg−1K−1
Specific heat capacity of water= 4200 JKg-1K-1
Heat required to raise the temperature of the ice to fusion point
H= 0.8 × 2060 × [0-(-35)]
H= 57680 J
Latent heat of fusion of ice;
H= mL
H= 0.8 ×3.36× 10^5
H= 2.688×10^5 J
Heat required to raise the temperature of the water to 100°C
Since mass is conserved, the mass of ice that has melted has been turned into an equivalent mass of water.
Therefore mass of water formed= 0.8Kg
H= 0.8× 4200 × 100
H= 336000J
Therefore total heat required;
H= 57680 + 2.688×10^5 + 336000
H= 662480 J
Answer:
2468,080j
Explanation:
Which best describes the direction of heat?
A team of landscapers pull an unplanted tree across the lawn. What forces are used?
Answer:
Explanation:
When an unplanted tree is pulled across the lawn then a variety of forces will be acting on the tree i.e.
1.There will be gravity force
2.Friction force to oppose the motion
3.Applied force which is pulling the tree
4. Normal force in response to the gravity force.
Jamal has a fan that plugs into the wall. When Jamal plugs in the fan and turns it on, the blades spin and make the air around them move.
Jamal's fan uses _______ energy to cause motion.
A.
electrical
B.
light
C.
sound
D.
heat
If you run the simulation a few times, you should see that for this particular pair of block and disc the block's position has the same numerical value as the disc's angular position, and the block's velocity has the same numerical value as the disc's angular velocity. Which of the following pairs of quantities must also have the same numerical values for the block and disc (assuming we use standard meter-kilogram-second units)? Select all that apply.
a. The work done by the force on the block and the work done by the torque on the disc.
b. The acceleration of the block and the angular acceleration of the disc.
c. The mass of the block and the mass of the disc.
d. The translational kinetic energy of the block and the rotational kinetic energy of the disc.
e. The momentum of the block and the angular momentum of the disc
Explanation:
C) is incorrect. The mass is equivalent to the moment of inertia in an angular formula.
The others appear all correct.
T * theta = F * r * theta = F * (r theta) = fx = work
This is the only one that needed explanation. The others should be obvious.
Which factor limits interference between waves? A constant phase relationship between waves Similar wave amplitudes Unequal wavelengths Radiation through the same region
Answer:
Unequal Wavelengths
Explanation:
Got it right on the exam
Unequal wavelengths limit interference between waves because the waves will have different frequencies and will not be able to form a stable interference pattern. When waves of different wavelengths interact, they will interfere constructively and destructively at different points, creating an unpredictable pattern.
Answer:
Unequal wavelengths
Explanation:
Got it correct on the quiz.
D’andre expends 120W of power in moving a couch 15 meters in 5 seconds. How much force does he exert?
Answer:
40N
Explanation:
What is clear cutting?
what property of an electromagnetic wave changes when the wave is encoded with analog information?
Answer:
Amplitude and Frequency
Explanation:
Analog signals are composed of continuous waves that can have any values for frequency and amplitude. These waves are smooth and curved.
Radio transmissions are a combination of two kinds of waves: audio frequency waves that represent the sounds being transmitted and radio frequency waves that "carry" the audio information. All waves have a wavelength, an amplitude and a frequency as shown in the figure. These properties of the wave allow it to be modified to carry sound information.
The two most common types of modulation used in radio are amplitude modulation (AM) and frequency modulation (FM). Frequency modulation minimizes noise and provides greater fidelity than amplitude modulation, which is the older method of broadcasting . Both AM and FM are analog transmission systems, that is, they process sounds into continuously varying patterns of electrical signals which resemble sound waves.
In one experiment, you measured the potential difference across a resistor as a capacitor discharged through it. You then plotted the natural logarithm of the voltage vs time (in seconds), and from the equation of the best fit line you measured the time constant of the RC circuit. If the equation of that line is ln open vertical bar V close vertical bar equals negative 0.027 t plus 2.5 , what is the time constant of the circuit?
Answer:
Explanation:
For discharge of capacitor in RC circuit , the relation is as follows
[tex]V=V_0e^\frac{-t}{\lambda}[/tex]
V is voltage across the capacitor , V₀ is maximum voltage across capacitor , λ is time constant and t is the time after which the voltage is recorded. During discharge this will also be voltage across resistance .
Taking log on both sides
lnV = lnV₀ - [tex]\frac{t}{\lambda}[/tex]
Given equation
[lnV] = - .027 t + 2.5
Comparing these equation
[tex]\frac{1}{\lambda} = .027[/tex]
λ = 37 s
time constant = 37 sec.
name 3 things in the solar system
Answer:
mercury ,venus, earth
Answer
sunplanets moonscometshope this helps
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Which medium (1 or 2) is more dense?
Answer:
The answer is 1
Explanation:
It's fr 1
Sinec the light rays bends away from the normal when it enters into medium 2, the denser medium is medium 1.
What is refraction?Refraction is the bending of light waves at the boundary of media of different densities.
During refraction, if light travels from less dense to a denser medium, the light rays is bent towards the normal.
However when light travels from denser to less dense medium, the light rays bends away from the normal.
Therefore, since the light rays bends away from the normal when it enters into medium 2, the denser medium is medium 1.
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According to recent typical test data, a Ford Focus travels 0.240 mi in 19.3 s, starting from rest. The same car, when braking from 62.5 mph on dry pavement, stops in 150 ft. Assume constant acceleration in each part of its motion, but not necessarily the same acceleration when slowing down as when speeding up.(a) Find the magnitude of this car's acceleration while braking.(b) Find the magnitude of this car's acceleration while speeding up.(c) If its acceleration is constant while speeding up, how fast (in mph) will the car be traveling after 0.250 mi of acceleration?(d) How long does it take the car to stop while braking from 59.0 mph?
Answer:
Explanation:
a )
While breaking initial velocity u = 62.5 mph
= 62.5 x 1760 x 3 / (60 x 60 ) ft /s
= 91.66 ft / s
distance trvelled s = 150 ft
v² = u² - 2as
0 = 91.66² - 2 a x 150
a = - 28 ft / s²
b ) While accelerating initial velocity u = 0
distance travelled s = .24 mi
time = 19.3 s
s = ut + 1/2 at²
s is distance travelled in time t with acceleration a ,
.24 = 0 + 1/2 a x 19.3²
a = .001288 mi/s²
= 2.06 m /s²
c )
If distance travelled s = .25 mi
final velocity v = ? a = .001288 mi / s²
v² = u² + 2as
= 0 + 2 x .001288 x .25
= .000644
v = .025 mi / s
= .0025 x 60 x 60 mi / h
= 91.35 mph .
d ) initial velocity u = 59 mph
= 86.53 ft / s
final velocity = 0
acceleration = - 28 ft /s²
v = u - at
0 = 86.53 - 28 t
t = 3 sec approx .
A train is 240 meters long and travels 20 m/s. How long does
it take to cross a 360-meter long bridge?
S
Answer:
=18 sec
Explanation:
240m=20m/s, find 360m
360×20÷240=30m/s
time=distance÷speed
240÷20=12sec
if 240=12sec,find 360
360×12÷240
=18 sec
Which of the choices is not a statement or direct application of the second law of thermodynamics? There are no 100% efficient heat engines. Heat energy naturally transfers from a high temperature substance to a low temperature substance. The change in internal energy of a system can be found by combining the heat energy added to a system minus the work done by the system. All natural processes tend toward states of increased entropy.
Answer:
Explanation:
Heat energy naturally transfers from a high temperature substance to a low temperature substance.
It is not a statement or direct application of the second law of thermodynamics.
The change in internal energy of a system can be found by combining the heat energy added to a system minus the work done by the system.
It is not a statement or direct application of the second law of thermodynamics. This statement is in accordance with first law of thermodynamics.
All the other two statements are in accordance with second law of thermodynamics.
The statement B is not a statement or direct application of the second law of thermodynamics.
Statements given to us:
(a.) There are no 100% efficient heat engines.
(b.) Heat energy naturally transfers from a high temperature substance to a low temperature substance.
(c.) The change in internal energy of a system can be found by combining the heat energy added to a system minus the work done by the system.
(d.) All natural processes tend toward states of increased entropy.
According to the Second Law of Thermodynamics:
heat transfer occurs spontaneously only from higher to lower temperature bodies.Entropy of the entire universe, as an isolated system, will always increase over time. The changes in the entropy in the universe can never be negative.So, according to the above points statement B is not a statement or direct application of the second law of thermodynamics.
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Which item stores the most electrical potential energy within its capacitors?
A) Cell phone
B) Tablet
C) Television
D) Heating and Cooling system
Answer:
C. Television
Explanation:
Mostly in cathode ray television, a TV has many of different types of capacitors, used as connections between circuits, as timing components and as electronic filters. TV capacitors perform many functions.
capacitor acts as a reservoir for electric charge, storing and releasing electricity in precise amounts.
What is a Capacitor ?
A capacitor is a simple device consisting of a pair of metal foils separated by a thin insulator, such as plastic, used basically for storing charge
Answer:
D) Heating and Cooling system
Explanation:
just took the test and got it right :)
A 385-g tile hangs from one end of a string that goes over a pulley with a moment of inertia of 0.0125 kg ⋅ m2 and a radius of 15.0 cm. A mass of 710 g hangs from the other end of the string. When the tiles are released, the larger one accelerates downward while the lighter one accelerates upward. The pulley has no friction in its axle and turns without the string slipping. What is the tension in the string on the side of the 710-g tile?
Answer:
the tension in the string is 5.59 N
Explanation:
Here ,
m_1 = 0.385 Kg
m_2 = 0.710 Kg
Using second law of motion ,
a = F_net / effective mass
a = (0.710- 0.385)×9.8/(0.710 + 0.385 + 0.0125/0.15^2)
a = 1.93 m/s^2
Now , let tension be T ,
then,
mg-T=ma
0.710×g - T = 0.710×1.93
T = 5.59 N
the tension in the string is 5.59 N
The invisible line that passes through the North Pole and the South
Pole is called Earth's what
Answer:
The Prime Meridian
The invisible line that passes through the North Pole and the South
Pole is called Earth's axis.
What is axis of earth?The imaginary line connecting the North and South poles is known as the Earth's axis. Its orbital plane and it are at an angle of 66 (1/2) degrees.
What is north pole and south pole?The Earth rotates on a 22 1/2-degree axis rather than vertically. A compass's arrow always points north when being used. The South Pole is located at the southernmost point on Earth, whereas the North Pole is located at its northernmost point. The region near the North and South Poles is extremely cold, whereas the region around the equator is extremely warm.
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How dose the Sum Of Forces help you
Answer:
The purpose of adding force vectors is to determine the net force acting upon an object. In the above case, the net force (vector sum of all the forces) is 0 Newton. ... We would say that the object is at equilibrium. Any object upon which all the forces are balanced (Fnet = 0 N) is said to be at equilibrium.
Explanation:
hope that helps you
A block is given an initial speed of 3m/s up a 25° incline coefficient of friction= 0.12
A) how far up the plane will it go?
B) how much time elapses before it returns to it's starting point?.
Answer:
a) y = 0.459 m , b) t = 13 s
Explanation:
a) For this exercise we use Newton's second law to find the acceleration of the block
we fix a reference system with the x axis parallel to the plane and the y axis perpendicular to it
X axis
-Wₓ - fr = m a (1)
Axis y
N - [tex]W_{y}[/tex] = 0
N = W_{y}
the friction force has the formula
fr = μ N
let's use trigonometry to find the components of the weight
sin 25 = Wₓ / W
Wₓ = W sin 25
cos 25 = W_{y} / W
W_{y} = W cos 25
we substitute in 1
- W sin 25 - μ W cos 25 = m a
- g (sin 25 - μ cos 25) = a
let's calculate
a = - 9.8 (sin 25 - 0.12 cos 25)
a - 0.25 m / s
this is the acceleration on the plane, so we can use the kinematic relations in one dimension
the highest point where the block rises the speed is zero (va = 0)
v² = v₀² - 2 a y
y = v₀² / 2g
y = 3 2 / (2 9.8)
y = 0.459 m
this is the distance the cantes block travels to stop
b) the time of the entire journey is
y = v₀ t - ½ a t²
the point where the body recesses is y = 0
0 = (vo - ½ a t) t
whose solutions are
t = 0
0 = vo - ½ a t
t = 2vo / a
t = 2 3 / 0.459
t = 13 s
A ball is thro.d hit the grouvelocity)?
Answer:
The velocity of the ball is 3.52 m/s.
Explanation:
A projectile is any object that moves under the influence of gravity and momentum only. Examples are; a thrown ball, a fired bullet, a kicked ball, thrown javelin, etc.
Given that the ball was thrown vertically upward on the top of a skyscraper of height 61.9 m. So that the velocity can be determined by;
u = [tex]\sqrt{\frac{2H}{g} }[/tex]
Where: u is the velocity of the object, H is the height and g is the gravitational force on the object. Given that: H = 61.9 m and g = 10 m/[tex]s^{2}[/tex], then;
u = [tex]\sqrt{\frac{2*61.9}{10} }[/tex]
= [tex]\sqrt{\frac{123.8}{10} }[/tex]
u = 3.5185
The velocity of the ball is 3.52 m/s.
Why do astronauts' weights differ in space?
There is a less gravitational force in space.
Their mass changes in space.
Space is colder than Earth.
There is less oxygen in space.
Answer:
There is less gravitational force in space.
Explanation:
Gravity doesn't exist as it does on Earth. Earth's gravity is as 6 times stronger as it is on the moon.
What kind of lens is found in both a magnifying glass and a microscope
Answer:
convex lens
Explanation:
The primary coil of a transformer has 200 turns and the secondary coil has 800 turns. The power supplied to the primary coil is 400 watts. What is the power generated in the secondary coil if it is terminated by a 20-ohm resistor? The primary coil of a transformer has 200 turns and the secondary coil has 800 turns. The power supplied to the primary coil is 400 watts. What is the power generated in the secondary coil if it is terminated by a 20-ohm resistor? 20W 200W 400W 800W 8000W 16000W 32000W\
Answer:
400 W
Explanation:
Ignoring the efficiency rating for the transformer we have to assume 100% .. Also, the power input to primary is equal to the power output in secondary.
This means that power input = 400 W = power output