) Water is leaking out of an inverted conical tank at a rate of 11,000 cm3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 12 m and the diameter at the top is 8 m. If the water level is rising at a rate of 30 cm/min when the height of the water is 2 m, find the rate at which water is being pumped into the tank. Give your answer in units of cm and min and round to the nearest whole number. (Write your answer in a complete sentence).
Answers
Answer:
Rate at which water is being pumped into the tank, \(R_{in} = 429933.33 cm^3/min\)
Explanation:
Rate at which water is leaking out, \(R_{out} = 11, 0000 cm^3/min\)
Height of the tank, h = 12 m
The top diameter of the tank, d = 8 m = 800 cm
The top radius of the tank, r = d/2 = 800/2 = 400 cm
The rate of change of water height, dh/dt = 30 cm/min
Height of water = 2 m
By carefully observing the diagram contained in the file attached to this solution, using the property of similar triangle:
h/r = 12/4
r = h/3
Since the tank is conical, volume of the water at time, t will be:
\(V = \frac{1}{3} \pi r^{2} h\\\\V = \frac{1}{3} \pi (\frac{h}{3} )^{2} h\\\\V = \frac{1}{27} \pi h^{3} \\\)
Finding the derivative of the above with respect to t to get the rate of change in the volume of water.
\(\frac{dV}{dt} = \frac{1}{9} \pi h^{2} \frac{dh}{dt} \\\\\frac{dV}{dt} = R_{in} - R_{out} \\\\\frac{1}{9} \pi h^{2} \frac{dh}{dt} = R_{in} - R_{out}\\\\\frac{1}{9} \pi * 200^{2}* 30 = R_{in} - 11000\\\\ R_{in} = 429933.33 cm^3/min\)
Related Questions
Air at 273K and 1.01x10³Nm2 pressure contains 2.70x1025 molecules per cubic meter. How many molecules per cubic meter will there be at a place where the temperature is 223K and pressure is 1.33x10 Nm-2
Answers
The molecules of O2 that are present in 3.90 L flask at a temperature of 273 K and a pressure of 1.00 atm is 1.047 x 10^23 molecules of O2
Step 1: used the ideal gas equation to calculate the moles of O2
that is Pv=n RT where;
P(pressure)= 1.00 atm
V(volume) =3.90 L
n(number of moles)=?
R(gas constant) = 0.0821 L.atm/mol.K
T(temperature) = 273 k
by making n the subject of the formula by dividing both side by RT
n= Pv/RT
n=[( 1.00 atm x 3.90 L) /(0.0821 L.atm/mol.k x273)]=0.174 moles
Step 2: use the Avogadro's law constant to calculate the number of molecules
that is according to Avogadro's law
1 mole = 6.02 x10^23 molecules
0.174 moles=? molecules
by cross multiplication
the number of molecules
= (0.174 moles x 6.02 x10^23 molecules)/ 1 mole =1.047 x 10^23 molecules of O2
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Highway safety engineers want to design roadside barriers that will crumple
in the event that a car drives off the road and collides with them, slowing
down the car more gradually. The average person has a mass of 68 kg and
travels on a highway at a velocity of 27 m/s. If the engineers know that the
maximum force that a person can safely withstand is 1650 N, approximately
how much time is required to crumple the barrier to safely slow the person
with this force?
A 1.5s
B. 0.7 s
C. 1.1 s
D. 2.1 s
Answers
The time required to crumple the barrier and safely slow down the person with a force of 1650 N is approximately C, 1.1 seconds.
How to find time?To determine the time required to crumple the barrier and safely slow down the person with a maximum force of 1650 N, use the equation of motion:
F = m × a
where:
F = force
m = mass
a = acceleration
Given:
m = 68 kg
F = 1650 N
Find the acceleration (a) first. Rearranging the equation:
a = F / m
Substituting the values:
a = 1650 N / 68 kg
a ≈ 24.26 m/s²
Now, use the equation of motion to find the time (t):
v = u + at
where:
v = final velocity (0 m/s as the person comes to a stop)
u = initial velocity (27 m/s)
a = acceleration (24.26 m/s²)
t = time
Rearranging the equation:
t = (v - u) / a
Substituting the values:
t = (0 m/s - 27 m/s) / 24.26 m/s²
t ≈ -27 m/s / 24.26 m/s²
t ≈ -1.11 s
The negative sign indicates that the time is in the opposite direction to the initial velocity. Taking the absolute value, the time required to crumple the barrier and safely slow down the person with a force of 1650 N is approximately 1.11 seconds.
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Why is the Falcon 9 rocket so important in today's space exploration world?
It's the first rocket to have been built by robots, saving money for labor costs.
Carbon fiber is used on the outside, making it much more lightweight, requiring less fuel to launch it.
It was invented with the ability to recharge itself by using solar panels.
It's a reusable rocket and has saved money by being reused over 60 times already.
Answers
The Falcon 9 rocket is so important in today's space exploration world because It's a reusable rocket and has saved money by being reused over 60 times already.
option D.
Why is the Falcon 9 rocket so important in today's space exploration world?The Falcon 9 rocket, is developed by SpaceX, and it holds a significant importance in today's space exploration world due to several key features and achievements, and some of the importance include the following;
ReusabilityCost-effectivenessAdvancements in rocket technologyPayload capacity and versatilityInnovation and competitionFrom the given options, we can conclude that the Falcon 9 rocket is so important in today's space exploration world because It's a reusable rocket and has saved money by being reused over 60 times already.
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1. A ball is at rest on the top of a hill (see the figure).
At the top of the hill, the ball will have [the maximum value of its, no, the minimum value of its] gravitational potential energy and [no, the maximum value of its] kinetic energy. If the ball rolls down the hill then, its [gravitational potential energy, kinetic energy] is converted to [gravitational potential energy, kinetic energy] when it gets to the ground.
2. Get your stopwatch ready and prepare to drop the object from the height h you selected in the previous step. You should drop the object so its [bottom, top, middle] part is initially at the height h. The initial speed of the ball [zero, 9.8 m/s, 9.8 m/s^2, depends on the height h] You'll need to measure the time from when the ball leaves your hand to exactly when it hits the ground [ for the first time it bounces, after it bounces and then comes to rest, both the first time and then after it bounces; then average the two times]
.
Answers
2. When dropping the object, you should drop it so its top part is initially at the height h. The initial speed of the ball will be zero since it starts from rest. To measure the time it takes for the ball to hit the ground, you should start the stopwatch when the ball leaves your hand and stop it when the ball hits the ground for the first time. It is recommended to perform multiple trials and calculate the average time to minimize errors.
give the relationship between current, Resistance and potential difference
Answers
Explanation:
Current can be defined as the rate of flow of electric charge along a conductor.
Resistance can be defined as the opposition to the flow of charged electrons or current, it's unit is OhmA carousel is (more or less) a disk of mass, 15,000 kg, with a radius of 6.14. What torque must be applied to create an angular acceleration of 0.0500 rad/s^2?round to 3 significant figures
(Plssss help me im suffering from severe brainrot)
Answers
To calculate the torque required to create an angular acceleration, we can use the formula:
Torque = Moment of Inertia × Angular Acceleration
The moment of inertia of a disk can be calculated using the formula:
Moment of Inertia = (1/2) × Mass × Radius^2
Given:
Mass = 15,000 kg
Radius = 6.14 m
Angular Acceleration = 0.0500 rad/s^2
First, calculate the moment of inertia:
Moment of Inertia = (1/2) × Mass × Radius^2
Moment of Inertia = (1/2) × 15,000 kg × (6.14 m)^2
Next, calculate the torque:
Torque = Moment of Inertia × Angular Acceleration
Torque = Moment of Inertia × 0.0500 rad/s^2
Now, let's plug in the values and calculate:
Moment of Inertia = (1/2) × 15,000 kg × (6.14 m)^2
Moment of Inertia ≈ 283,594.13 kg·m^2
Torque = 283,594.13 kg·m^2 × 0.0500 rad/s^2
Torque ≈ 14,179.71 N·m
Rounding to three significant figures, the torque required to create an angular acceleration of 0.0500 rad/s^2 is approximately 14,180 N·m.
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3. A car with a mass of 1600 kg has a kinetic energy of 125 000 J. How fast is it moving?
Answers
The car is moving at approximately 12.5 meters per second.
The kinetic energy (KE) of an object can be calculated using the formula:
KE = 1/2 * m * \(v^2\)
where
KE = kinetic energy,
m =Mass of the object, and
v = velocity.
In this case, we are given the mass (m) of the car as 1600 kg and the kinetic energy (KE) as 125,000 J. To find the velocity .
Substituting the values , we have:
125,000 J = 1/2 * 1600 kg *\(v^2\)
Now, we can solve for v by rearranging the equation:
\(v^2\) = (2 * 125,000 J) / 1600 kg
\(v^2\) = 156.25 \(m^2/s^2\)
Taking the square root, we find:
v = √156.25\(m^2/s^2\)
v ≈ 12.5 m/s
Therefore, the car is moving at approximately 12.5 meters per second.
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PLEASE ANSWER FASG I WILL MARK BRAINELIST PLEASEEEEE
The number of protons in the nucleus of an atom determines the species of the atom, i.e., the element to which the atom belongs. An atom has the same number of protons and neutrons. But the electron number cannot be used instead because (5 points)
a. electrons are not within the nucleus
b. electrons are negatively charged
c. electrons can be removed from or added to an atom
d. electrons are lighter than protons
Answers
The electron number cannot be used instead because electrons can be removed from or added to an atom (option C)
Why the electron number cannot be used instead?The element of an atom is determined by its proton count, while the electron count can exhibit variability. Take, for instance, a sodium atom, which encompasses 11 protons and 11 electrons. However, it has the capacity to relinquish one electron, transforming into a sodium ion housing only 10 electrons.
This occurs due to the relatively loose binding of electrons to the nucleus, enabling their removal through the influence of an electric field or alternative mechanisms.
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B) Show that the equation for pressure p=F/ A' is dimensionally correct.
Answers
P = [M1 L1 T-2] × [L2]-1 = M1 L-1 T -2. Therefore, the pressure is dimensionally represented as M1 L-1 T -2.
Ball A with a mass of 0.280kg makes an elastic head-on collision with ball B initially at rest. After collision, ball B moves off with half the original speed of ball A. Is the momentum conserved in the collision? Why?
Answers
The mass of ball B and the final velocity of ball A can complement the conservation of linear momentum. The answer is yes.
What is Momentum ?Momentum can simply be defined as the product of mass and velocity. It is a vector quantity.
Given that ball A with a mass of 0.280kg makes an elastic head-on collision with ball B initially at rest. After collision, ball B moves off with half the original speed of ball A.
In an elastic head-on collision, momentum is mostly always conserved. That is, the sum of the momentum before collision will be equal to the sum of the momentum after collision.
Mathematically, MaUa = MaVa + MbVb
Is the momentum conserved in the collision?
The answer is yes!
Why?
Because we need to consider the mass of the ball B and the final velocity of the ball A.
Therefore, In consideration of the mass of the ball B and the final velocity of the ball A, we can say that the momentum is conserved.
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1.) A roller coaster travels on a frictionless track as shown in the illustration.
a.) If the speed of the car at Pt A is 5.0 m/s, what is the speed at Pt B
(More in the photo provided)
Answers
For the roller coaster on a frictionless track:
a. The speed at Point A is 5.0 m/s, the speed at Point B will also be 5.0 m/s.b. The height between Points A and B where kinetic energy equals potential energy is 5.0 m.c. For the car to reach Point C, the height at Point B must be greater than or equal to 8.0 m.d. For the car to reach Point C, the height at Point A must be greater than or equal to 8.0 m.How to solve speed and height?a. The speed of the car at Point B can be determined using the principle of conservation of energy. The total mechanical energy (sum of kinetic energy and potential energy) remains constant in the absence of external forces like friction. Therefore, if there is no energy loss, the kinetic energy at Point A is equal to the kinetic energy at Point B.
Given that the speed at Point A is 5.0 m/s, the speed at Point B will also be 5.0 m/s.
Answer: A. 5.0 m/s
b. To find the height at which kinetic energy equals potential energy, we can set the equations for kinetic energy and potential energy equal to each other.
At Point A, the roller coaster has both kinetic energy and potential energy. The total mechanical energy is the sum of these two:
Initial mechanical energy at Point A = Kinetic energy at Point A + Potential energy at Point A
At Point B, the roller coaster will have kinetic energy and potential energy, but we want to find the height at which kinetic energy equals potential energy. Let's call this height "h."
Mechanical energy at Point B = Kinetic energy at Point B + Potential energy at Point B
Since the speed at Point B is the same as the speed at Point A (5.0 m/s), the kinetic energy at both points is the same.
Equating the mechanical energy at Point A to the mechanical energy at Point B:
Initial mechanical energy at Point A = Mechanical energy at Point B
Kinetic energy at Point A + Potential energy at Point A = Kinetic energy at Point B + Potential energy at Point B
Since the kinetic energy is the same at both points, simplify the equation:
Potential energy at Point A = Potential energy at Point B
The potential energy at any point is given by the formula mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.
Therefore, at the height h between Points A and B, the potential energy equals the potential energy at Point A:
mgh = mghA
Since the mass and acceleration due to gravity are the same, cancel them out:
h = hA
This means that the height where kinetic energy equals potential energy is the same as the height at Point A.
Answer: The height between Points A and B where kinetic energy equals potential energy is 5.0 m.
c. To determine if the car will reach Point C, compare the potential energy at Point B with the potential energy at Point C. If the potential energy at Point B is greater than or equal to the potential energy at Point C, the car will reach Point C.
Potential energy at Point B = mghB
Potential energy at Point C = mghC
Given that the height at Point C is 8.0 m, compare the potential energies:
Potential energy at Point B ≥ Potential energy at Point C
mghB ≥ mghC
Since the mass (m) and acceleration due to gravity (g) are constant, cancel them out:
hB ≥ hC
Therefore, for the car to reach Point C, the height at Point B must be greater than or equal to 8.0 m.
d. The minimum speed needed at Point A for the car to reach Point C can be determined by comparing the potential energy at Point A with the potential energy at Point C. If the potential energy at Point A is greater than or equal to the potential energy at Point C, the car will have enough energy to reach Point C.
Potential energy at Point A = mghA
Potential energy at Point C = mghC
Given that the height at Point A is 5.0 m, compare the potential energies:
Potential energy at Point A ≥ Potential energy at Point C
mghA ≥ mghC
Since the mass (m) and acceleration due to gravity (g) are constant, cancel them out:
hA ≥ hC
Therefore, for the car to reach Point C, the height at Point A must be greater than or equal to 8.0 m.
To summarize, for the car to reach Point C, the height at Point B must be greater than or equal to 8.0 m, and the height at Point A must also be greater than or equal to 8.0 m.
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Which transforms radiant energy into sound energy.
Electric Heater
Cell Phone
Rolling a ball
Answers
Answer:
the answer is cell phone
What are the differences between atoms, molecules, and compounds?
Answers
Answer:
Atoms are the thing that make up molecules and compounds. Molecule. Two or more atoms joined together with covalent bonds. Molecules contain two or more atoms and are held together by covalent bonds, whereas compounds are held together by ionic bonds. Compound. Two or more elements bonded together through ionic attraction.
Is it possible that the physical velocity is constant but the magnitude of the velocity is variable?give an example
Answers
Answer:
yes it is possible
Explanation:
if the body is travelling with uniform speed in a circular track its speed remains the same but the velocity is non-uniform as the direction of the body is changing every time.
eg: a body in uniform circular motion has constant speed but its velocity changes at every point during the course of motion. Whenever, the direction changes, velcoity changes.
Question 1 of 20
Calculate: (9 x 10^8) divided (3 x 10^4) =
A. 6 x 10^4
B. 3 x 10^4
C. 3 x 10^4
D. 6 x 10^2
Answers
How do electrons conduct electricity?Please explain in terms of charges
Answers
The electrons are usually at a constant distance from the nucleus of an atom in precious shells. The flow of charges to the per unit of time helps the conductor to conduct electricity. The mathematic representation of the electric current is given in the terms of charges as
\(I=\frac{q}{t}\)*Here 'q' is the charge
*Here 't' is the time
The movement of electrons
The flow of charges inside the metal (conductor) is known as the electric current.
A rocket ship has several engines and thrusters. While the Solid Rocket Booster (SRB) and main engines only work together during the first 2 minutes of flight, the main engines operate for a total of 8.5 minutes after the launch. Once the SRBs are released, the main engines alone accelerate the rocket from about 1341 m/s to 7600 m/s.
What is the acceleration of the SRB and main engine during the first 2.0 minutes of flight?
A. 52 m/s2
B. 13 m/s2
C. 9.8 m/s2
D. 11 m/s2
Answers
The acceleration of the SRB and main engine during the first 2.0 minutes of flight is 52.16 m/s².
The given parameters;
initial velocity of the engine, u = 1341 m/sfinal velocity of the engine, v = 7600 m/stime of motion, t = 2 minutes = 2 x 60 s = 120 sThe acceleration of the SRB and main engine is calculated as follows;
\(a = \frac{\Delta v}{\Delta t } \\\\a = \frac{7600 - 1341}{2 \times 60 s} \\\\a = 52.16 \ m/s^2\)
Thus, the acceleration of the SRB and main engine during the first 2.0 minutes of flight is 52.16 m/s².
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Can someone help me grasp the concept of solving this please
Answers
Answer:
Q= m × c × change in tempQ= 1000 cal/kg × C Q= (5kg) × (1000 ) × (100-13) Q= 435000Hence 4.35 × 10^5 Ask any questions!I also do quizzes and exams if your interested!Find the depth in a lake at which the pressure is 173.693 lb/in2.
Answers
The depth in the lake of pressure 173.693 lb/in² is 122.45 m.
What is depth?Depth is the distance down either from the top of something to the bottom, or to a distance below the top surface of something.
To calculate the depth in the lake, we use the formula below.
Formula:
h = P/gD........................ Equation 1Where:
h = Depth in the lakeP = Pressure D = Density of waterg = Acceleration due to gravityFrom the question,
Given:
P = 173.693 lb/in² = 1.2×10⁶ N/m²g = 9.8 m/s²D = 1000 kg/m³Substitute these values in to equation 1
h = (1.2×10⁶)/(9.8×1000)h = 122.45 mHence, the depth in the lake is 122.45 m.
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A wave is moving at a velocity of 8 km/sec with a frequency of 10 Hz.
Use the equation you rearranged to determine the wavelength of the wave.
Answers
Explanation:
arn core concepts.
See Answer
1) For a P wave with velocity of 8 km/s (typical upper mantle speed) in a Poisson solid,compute the wavelength for waves with periods of:
a) 15 sec
b) 1 sec
c) 0.1 sec (100 Hz)
2) Repeat question 2 for an S wave in the same medium (Hint: you have to determine the S wave speed).
how many taste buds do humans have 100,000, 100, 10,000 1,000
Answers
The approximate number of taste buds that humans have is 10,000 (option C).
What are taste buds?Tastebuds are any of the small organs on the tongue used for tasting.
Taste buds are cells on the tongue that allow one to perceive tastes, including sweet, salty, sour, bitter and umami.
Taste buds regenerate approximately every 10 days, which means injured taste buds usually repair on their own. The average adult human has between 2000 and 8000 tastebuds.
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A 2 column table with 4 rows. The first column was labeled drink with entries hot chocolate, milk, juice, water. The second column is labeled temperature in degrees Celcius with entries 50, 35, 40, 15.
List these drinks in order of kinetic energy, starting with the drink whose particles have the highest kinetic energy.
hot chocolate, water, juice, milk
hot chocolate, juice, milk, water
water, milk, juice, hot chocolate
water, hot chocolate, juice, milk
Answers
List these drinks in order of kinetic energy, starting with the drink whose particles have the highest kinetic energy:
hot chocolate > juice > milk > water.
What is temperature?The average kinetic energy of the particles in an object is measured by its temperature. The velocity of these particles likewise increases as the temperature rises.
A thermometer or a calorimeter is used to determine the temperature. In other words, a system's internal energy is determined by its temperature.
Hence, the kinetic energy of molecules is proportional to temperature of the liquid. So, list these drinks in order of kinetic energy:
hot chocolate > juice > milk > water.
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A 150-pound person uses 6.2 calories per minute when walking at a speed of 4 mph. How long must a person walk at this speed to use at least 230 calories?
Answers
The time taken by person to use 6.2 calories is 1 min.
Therefore, the time taken to use 230 calories can be calculated as,
\(\begin{gathered} t=\frac{(230\text{ calories)(1 min)}}{(6.2\text{ calories)}} \\ \approx37.1\text{ min} \end{gathered}\)Thus, the time taken to use 230 calories is 37.1 min.
A man yells across a canyon to his friend who hears the yell 3.25 seconds later. How far away is the man's friend? (speed of sound in air = 343 m/s)
Answers
The man's friend is at a distance 552.5 m away.
Speed of sound in air, v = 340 m/s
Time after which the echo is heard, t = 3.25 s
The expression for the total distance covered by the sound in the given time,
d = v x t
d = 340 x 3.25
d = 1105 m
Therefore, the distance where the friend is staying would be half of the total distance covered by the sound during the given time.
So, the distance of the friend from the man,
d' = d/2
d' = 1105/2
d' = 552.5 m
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Sanjeev noticed his plants were wilting and turned on the sprinklers in his garden. An hour later, he notices that the plant's leaves aren’t wilted any longer. Why did this happen?
A) The xylem stored the water in the stem of the plant, making it more rigid
B) The water flowed out of the vacuole creating turgor pressure in the plant’s cells
C) The plant’s stored energy was activated by the water
D) The water entered the vacuole creating turgor pressure in the plant’s cells
help please ASAP
Answers
Answer:
B
Explanation:
Answer:
D
Explanation:
P.E
1. Tukuyin ang mga galaw sa kahon kung ito ay pag-galaw sa low level, middle level o high
level. Isulat ang iyong sagot sa teybol sa ibaba.
pag-upo
paglakad
pagtakbo
pagdapa sa sahig
pagtalon
Answers
Answer:
pagtalon?
Explanation:
because that had to be the answer
To what extent do you believe that Jews, christians, and Muslims use the divine command theory approach rather than egoism or act or rule utilitarianism as a basis for their ethical system
Answers
Jews, christians, and Muslims use the divine command theory rather than egoism or act or rule utilitarianism as a basis for their ethical system because of their belief that things are right because God commands them to be.
What is the idea behind the theory of divine commands?According to the Divine Command Theory, the ethically correct course of action is the one that God requires or commands because morality ultimately rests on God's instructions or character.
The idea that something is right because God has ordered it to be thus is known as the divine command theory. In other words, it implies that morally repugnant or immoral actions are wrong because God forbids them. This theory is absolutist.
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Which of the following types of stars is hottest?
A
B
C
D
Answers
Answer:
graph b
Explanation:
Are you better off in an accident where the hood is
deformed or where the car is not damaged at all but
bounces backward?
Answers
Answer:
you would be better off if the car bounced backwards
Explanation:
because if the hood was dismembered than you have a high chance of very bad injury but if it is just bounced back you would have less chance of getting hurt if properly sitting and seat belted.
A DC electric motor transforms 5.3 kW of electrical power into mechanical form. If the motor's operating voltage is 250 volts, how much current does it "draw"?
Answers
The current drawn in the circuit by the DC electric motor is found to be 21.2 amperes.
Explain about the electrical power?Electric power is a standard measure for how quickly electrical energy is delivered over an electric circuit.
P represents for power, which is denoted and measured and use the SI unit of power, the watt, or a joule per second. Electric batteries and electric generators are frequently used to produce and supply electricity. The movement of electrical power as well as charge is known as electricity.Power of electric motor P = 5.3 KW = 5300 W
Operating Voltage V = 250 volts
Power = Current * voltage
P = V * I
I = P / V
I = 5300 / 250
I = 21.2 A
Thus, the current drawn in the circuit by the DC electric motor is found to be 21.2 amperes.
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