The banking angle of the curved part of the speedway is determined as 32⁰.
Banking angle of the curved road
The banking angle of the curved part of the speedway is calculated as follows;
V(max) = √(rg tanθ)
where;
r is radius of the pathg is acceleration due to gravityV² = rg tanθ
tanθ = V²/rg
tanθ = (34²)/(190 x 9.8)
tanθ = 0.62
θ = arc tan(0.62)
θ = 31.8
θ ≈ 32⁰
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In a science museum, a 110 kg brass pendulum bob swings at the end of a 13.9 m -long wire. the pendulum is started at exactly 8:00 a.m. every morning by pulling it 1.2 m to the side and releasing it. because of its compact shape and smooth surface, the pendulum's damping constant is only 0.010kg/s.
at exactly 12:00 noon, how many oscillations will the pendulum have completed?
what is its amplitude at noon?
The number of oscillations completed by the pendulum is 2736.
The amplitude of the pendulum is 3.47 m.
The given motion is an underdamped motion. So its frequency will be similar to that of a simple harmonic motion.
The frequency of oscillation is defined as the number of oscillations completed in unit time. It is calculated using the formula.
f=(1/2π)*√(l/g)
where f is the frequency, l is the length of the pendulum, and g is the acceleration due to gravity.
Given the length of the wire l=13.9 m and acceleration due to gravity g=9.8 m/s^2. The frequency of oscillation is:
f=(1/(2*3.14)) * √(13.9/9.8)
f=0.19 Hz (approximately)
Since the pendulum started oscillating at 8:00 am, 4 hours has been passed when it shows 12:00 pm. So time t=4 hours or t=4*3600. Hence t=14400 s. The total number of oscillations is then given by the formula,
n=ft
where n is the number of oscillations.
n=0.19*14400=2736.
In damping motion, the amplitude of the pendulum decreases with time. The amplitude of the pendulum is given by the formula,
A' = A exp (-b*t)
where A' is the amplitude after time t, A is the initial amplitude, b is the damping constant, and t is the time.
Here A=1.2 m, b=0.010 kg/s and t=14400 s.
A' = 1.2 exp (-0.010*14400)
A'=3.47 m (approximately)
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A ball rolls from x=3.85m to x=22.1m in 5 seconds. What was its average velocity
Answer:
Average Velocity = 3.65 m/s
Explanation:
Average Velocity [tex]=\frac{Total Displacement}{Total Time}[/tex] [tex]=\frac{22.1-3.85}{5}=\frac{18.25}{5}=3.65[/tex]
The average velocity of a ball that rolls from x=3.85m to x=22.1m in 5 seconds is -3.65 m/s.
Given the following values:
Initial position, x = 3.85 m
Final position, x'= 22.1 m
Initial time, t = 0 seconds
Final time, t'= 5 seconds
The average velocity can be computed from the ratio of change in displacement and time.
The average velocity is given as:
v = (x'-x)/(t'-t)
v = (22.1-3.85)/(5-0)
v = -3.65 m/s
Hence, the average velocity of a ball that rolls from x=3.85m to x=22.1m in 5 seconds is -3.65 m/s.
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An object is moving with a force 30N then hits a wall to a stop in 0.5s.
a. Calculate the impulse.
b. What is the change in momentum of the object?
The impulse and change in momentum of an object moving with a force 30N then hits a wall to a stop in 0.5s is 15Ns.
How to calculate impulse?Impulse is the integral of force over time. It is calculated by multiplying the force applied by the time as follows:
∆p = Force × time
According to this question, an object is moving with a force 30N and then hits a wall to a stop in 0.5s.
Impulse = 30N × 0.5s = 15Ns
Therefore, the impulse and change in momentum of an object moving with a force 30N then hits a wall to a stop in 0.5s is 15Ns.
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Find the Y upon DX for the following functions why is equal to bracket X -1 bracket X -2 upon route x
Rewrite the equation as
[tex]y = (x-1) (x-2) x^{-1/2}[/tex]
Then by the product rule, the derivative is
[tex]\dfrac{dy}{dx} = (x-2) x^{-1/2} + (x-1) x^{-1/2} - \dfrac12 (x-1) (x-2) x^{-3/2}[/tex]
and we can factorize this as
[tex]\dfrac{dy}{dx} = \dfrac12 x^{-3/2} \left(2 (x-2) x^{3/2-1/2} + 2 (x-1) x^{3/2-1/2} - (x-1) (x-2)\right)[/tex]
[tex]\dfrac{dy}{dx} = \dfrac12 x^{-3/2} \left(2 (x-2) x + 2 (x-1) x - (x-1) (x-2)\right)[/tex]
[tex]\dfrac{dy}{dx} = \dfrac12 x^{-3/2} (3x^2 - 3x - 2)[/tex]
[tex]\dfrac{dy}{dx} = \dfrac{3x^2 - 3x - 2}{2x^{3/2}}[/tex]
and optionally expanded once more (if only to match the provided "Ans") to
[tex]\dfrac{dy}{dx} = \dfrac32 x^{2-3/2} - \dfrac32 x^{1-3/2} - x^{-3/2}[/tex]
[tex]\dfrac{dy}{dx} = \dfrac32 x^{1/2} - \dfrac32 x^{-1/2} - x^{-3/2}[/tex]
[tex]\dfrac{dy}{dx} = \dfrac32 \sqrt x - \dfrac3{2\sqrt x} - \dfrac1{\sqrt{x^3}}[/tex]
A sports car starts from rest it covers a distance of 900 m to attain a speed of 80m s determine the acceleration of the car and the time required to reach this speed
The acceleration of the car and the time required to reach this speed will be 8 m/s² and 10 sec.
What is acceleration?The rate of velocity change concerning time is known as acceleration.
Given data;
Initial velocity, u=0 m/s
Final velocity, v= 80 m/sec
Distance travelled,s =900m
From Newton's third equation of motion;
v²=u²+2as
a =(v²-u²)/2s
Substitute the given values;
a = (80²-0)/2 ×900
a = 6400/1800
a=8 m/s²
The time required to reach this speed is found in Newton's first equation of motion as;
v = u+at
Substitute the given values;
80 = 0 + 8t
t=80/8
t = 10 sec
Hence, the acceleration of the car and the time required to reach this speed will be 8 m/s² and 10 sec.
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What type of circuit have you made?
The type of circuit which have been made is the series circuit in this scenario.
What is a Series circuit?
This is a complete path which involves the whole electric current flowing through the various parts such as resistor etc..
There is only one path of current in which it does not undergo any form of split during motion.
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A large glass marble is added to the displacement can. 20 3 of water overflows into a beaker, and the displacement can now has a mass of 872 .
Calculate the density of glass.
The density of the glass can be determined using the formula:
Density of the glass = (Mf - Mi)/20 cm³What is density?Density is defined as the ratio of mass and volume of a substance.
Density = mass/volumeThe mass of the glass = Final mass of beaker - initial mass of beaker (Mf - Mi)
The initial mass of the beaker is not given.
Volume of the glass marble = 20 cm³
Density of the glass = (Mf - Mi)/20 cm³
Therefore, the density of the glass is determined from the ratio of the mass and volume of the glass.
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Consider the following situations:
A. A 2.5 kg physics book is resting on the edge of a table 1.4 m above the floor
B. A 10.0 kg backpack is on the floor beside the door
C.A 1 kg backpack is on the shelf that is 2.0 m above the floor
In which situation(A, B or C) is the potential energy the most?
OA
O
O
A, B and C all have the same potential energy
C
B
Given the data from the question, the potentiel energy is most in A
To obtain the correct answer to the question, we shall determine the potential energy in each case
How to determine the potential energyPE = mgh
Where
PE is the potential energym is the massg is the acceleration due to gravityh is the heightCase A
Mass (m) = 2.5 KgHeight (h) = 1.4 mAcceleration due to gravity (g) = 9.8 m/s²Potential energy (PE) = ?PE = mgh
PE = 2.5 × 9.8 × 1.4
PE = 34.3 J
Case B
Mass (m) = 10 KgHeight (h) = 0 mAcceleration due to gravity (g) = 0 m/s²Potential energy (PE) = ?PE = mgh
PE = 2.5 × 0 × 0
PE = 0 J
Case C
Mass (m) = 1 KgHeight (h) = 2 mAcceleration due to gravity (g) = 9.8 m/s²Potential energy (PE) = ?PE = mgh
PE = 1 × 9.8 × 2
PE = 19.6 J
SUMMARY
Potential energy in case A = 34.3 JPotential energy in case B = 0 JPotential energy in case C = 19.6 JThus potential energy is most in A
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ust before it exploded, the star that became supernova 1987A was a(n) Group of answer choices B3 supergiant. white dwarf. M2 supergiant. pulsar.
Option (a) B3 supergiant is correct.
Just before it exploded, the star that became supernova 1987A was a B3 supergiant.
Any star with extremely high intrinsic luminosity and relatively vast size is referred to as a supergiant star.
B3 supergiant is a blue supergiant.
An OB supergiant, often known as a blue supergiant (BSG), is a hot, brilliant star like Rigel.
The hottest stars in the universe are blue supergiants, with temperatures ranging from 10,000 K to 50,000 K or higher.
A type II supernova known as SN 1987A occurred in the Milky Way's dwarf satellite galaxy, the Large Magellanic Cloud.
Red supergiants are the most frequent supernova progenitors, and it was once thought that only red supergiants could explode as supernovae. However, because SN 1987A's parent star, was a B3 blue supergiant, this notion had to be reexamined.
Hence, just before it exploded, the star that became supernova 1987A was a B3 supergiant.
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A block slides down an inclined plane. Which force does zero work? I. Weight II. Friction III. Normal
II. The work done by frictional force is zero.
What is work done?Work is said to be done when an applied force moves an object over a given distance.
Work done by friction = μ(Fn)d
where;
μ is coefficient of frictionFn is normal forceSince the frictional force could not prevent the block from sliding, we can conclude that the work done by frictional force is zero.
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Sunlight reflects from a concave piece of broken glass, converging to a point 18 cm from the glass. What is the radius of curvature of the glass
Radius of curvature of the concave mirror is 36 cm.
To find the answer, we need to know about the relation between focal length and radius of curvature.
What's the relation between the radius of curvature and focal length?Mathematically, focal length= radius of curvature/2Radius of curvature= 2× focal lengthWhat's the focal length of the concave mirror when sunlight converges to 18cm?When light from a far distance incident on a concave mirror, it converges to the focus point.As the sun light comes from very far distance, so it is converging to the focus point. So focal length= 18 cm.What's the radius of curvature of the concave mirror?Here, radius of curvature= 2×18 cm = 36cm
Thus, we can conclude that the radius of curvature of the concave mirror is 36cm.
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A footballer kicks a ball at angle teta to horizontal with some initial velocity a) what are the two types of independent motion takes place at the same time? b.how long is the ball in the air?
a) The motion along the vertical direction and the motion along the horizontal direction.
b) The object remains in the air for a time period of 2usin(θ)/g.
Any object that is thrown in the air when gravity is acting on it is called a projectile. The motion of this projectile is called projectile motion.
When the projectile is thrown in the air at some angle θ, then there are two independent motions taking place at the same time. First is the component of motion along the vertical direction along which gravity acts. Second is the component of motion along the horizontal direction along which the object moves with a constant velocity. No force acts along the horizontal direction. The horizontal motion does not affect the vertical motion and the converse is also true. So these are independent of each other.
The time of flight is the time during which a projectile remains in the air. This time of flight is calculated using the formula,
T=2usin(θ)/g
where T is the time of flight, u is the initial velocity and g is the acceleration due to gravity.
Hence, the object remains in the air for a time period of 2usin(θ)/g.
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A positive charge traveling north enters a region where the electric field is uniform and points east. This charge will Group of answer choices continues with the same speed in the same direction slows down speed up veers east veers west
Option D is correct : This positive charge will veer east
It is given that the particle has a positive charge.
So, the direction of the force on the positive charge (and also the acceleration) is in the same direction as the electric field.
Now the electric field is uniform and points in east, the force on it [tex]F=qE[/tex]will also be pointed towards the east.
The positive charge was initially moving north, which means that the velocity vector was in the direction of north and when a positive charge first reaches an area with an electric field and force pointing east, its velocity vector will change to be along the electric field, or east.
That’s why a positive charge traveling north enters a region where the electric field is uniform and points east will veer east.
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Please Help!
The info below shows a kettle with its powers and the time they take to boil 500cm3 of water. If electricity costs 9p per unit, how much does it cost to boil 500cm3 of water using the 1.4kW kettle?
Kettle1= 1.4kW =4.5minutes
The cost of the 1.4KW kettle is 0.945 p.
What is the cost of electricity?The cost of electricity is computed from the cost of electricity. We have to know the cost of electricity that is charged for the 1.4kW kettle.
Now let the power consumed=
1.4kW * 0.075 hrs = 0.105 KWhr
Then;
1 KWhr costs 9p
0.105 KWhr costs 0.105 KWhr * 9p/1 KWhr
= 0.945 p
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What explains the dramatically different magnitudes of accelerations that result when a mosquito collides head on with a moving truck
Answer:
Mass of the vehicle and small bug.
Explanation:
By Newton's third law, force on bug and vehicle will be same when they collide with each other irrespective of their masses.But according to Newton's second law, force is mass times acceleration. Since the force on each mass is same, the smaller mass will accelerate more and the heavier mass will accelerate less for the same force.Therefore the acceleration of bug will be very greater than vehicle as the mass of the bug is very small as compared to vehicle.Learn more about Newton's law.
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A football wide receiver runs out from the line of scrimmage, turns around and runs 2 meters back toward the quarterback. Compared to the total distance covered by the player, the magnitude of the player's overall displacement is ______________.
Answer:
See below
Explanation:
TOTAL distance = x meters (not given how far he ran from scrimmage line)
Displacement = x - 2 meters ( although football uses yards not meters)
It is observed that in water the meniscus in the capillary tube is higher than the meniscus in the beaker,while in mercury the meniscus is lower than the meniscus in the beaker.explain these observations
Meniscus formed by water and mercury (In capillary tube and beaker):
Because the water wets the glass and seeps up the tube's side when it is contained in a glass tube, the meniscus (surface) of the water has a concave form. And in mercury, the meniscus is lower than the meniscus in the beaker because the intermolecular force between the mercury atom is stronger than the force within a wall of a container which is why mercury forms a lower meniscus.
What are meniscus?:
The meniscus arises when the liquid and the container walls have different attractive forces acting on the molecules of the liquid.
A meniscus is created through adhesion, which is related to water's relatively high surface tension. The molecules in the glass beaker's wall are drawn to the water molecules. Whereas cohesion is the intermolecular attraction of similar molecules.
In water the meniscus in the capillary tube is higher than the meniscus in the beaker: Because the glass pulls on the water molecules with a slightly stronger force than that which exists between the water molecules, the water and glass meniscus has a downward curvature. The glass's side is being dragged up with water. While in mercury the meniscus is lower than the meniscus in the beaker: Because the mercury atoms are more strongly attracted to one another than the glass is to the mercury atoms, thus it results in an upwardly curved meniscus.
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A duck flies in a straight line for 500m (60° N of W)
a.) What angle is this in polar coordinates?
b.) What is the North/South and East/West components of its displacement?
Please help me t-t
(A) The angle of this in polar coordinates is 30⁰.
(B) The North/South and East/West components of its displacement is 250 m and 433 m respectively.
The angle is this in polar coordinates60° N of W lies in the fourth quadrant;
θ = 90 - 60 = 30⁰
in polar coordinate = (r,θ) = (500 m, 30⁰)
Vertical component of the displacement (North/South)Dy = D sinθ
Dy = 500 m x sin(30) = 250 m
Horizontal component of the displacement (East/West)Dx = D cosθ
Dx = 500 m x cos(30) = 433 m
Thus, the angle of this in polar coordinates is 30⁰.
The North/South and East/West components of its displacement is 250 m and 433 m respectively.
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What braking technique slows the vehicle as quickly as possible without locking brakes or losing traction
Answer: Cadence braking or Stutter braking is the braking technique slows the vehicle as quickly as possible without locking brakes or losing traction.
Explanation: To find the answer, we need to know more about the Cadence breaking.
What is cadence braking?It's a braking technique, that includes, pumping the brake pedal and which used to allow a vehicle to steer as well as brake on a slippery surface.It is used in the case of an emergency or sudden braking is needed.In this technique, traction is limited to reduce the effect of skidding from road wheels locking up under braking.Thus, from the above given data, we can conclude that, Cadence braking or Stutter braking is the braking technique slows the vehicle as quickly as possible without locking brakes or losing traction.
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A spring with a spring constant of 59.5 N/m is attached to different masses, and the system is set in motion. What is its period for a mass of 2.3 kg
Time period for the mass 2.3 kg is 1.23s.
To find the answer, we need to know about the time period of a spring mass system.
What's the expression of time period of a spring mass system?Mathematically, time period= 2π/ angular frequencyAs angular frequency= √(k/m),time period= 2π×√(m/k)
k= spring constant and m= massWhat's the time period, if the spring constant and mass are 59.5N/m and 2.3 Kg respectively?Time period= 2π×√(2.3/59.5)
= 1.23 s
Thus, we can conclude that the time period of the spring mass system is 1.23 s.
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The figure below shows a ball on a curved surface. The ball is released at point A. At which point does the ball have maximum gravitational potential energy?
Answer:
Point A
Explanation:
Because it reaches maximum height
The law of combining volumes only applies under these conditions EXCEPT :_________.
i. the pressure must be the same. ii. the temperature must be the same. iii. the reactants must be liquids. iv. all reactants must be gases.
Answer:
measured at constant temperature and pressure
Hope this helps :)
what are the wave model and particle model of light
Answer:
Newton's corpuscular theory stated that light consisted of particles that travelled in straight lines. Huygens argued that if light were made of particles, when light beams crossed, the particles would collide and cancel each other. He proposed that light was a wave.
fill in the blank ,if a charge body touches the disc of an uncharged electroscope the leaves ------------------
Answer:
leaves will deverge
Explanation:
because of the nagwtive charge will become positive
You push a heavy crate down a ramp at a constant velocity. Only four forces act on the crate. Which force does the greatest magnitude (it does not matter positive or negative) of work on the crate
The friction force does the greatest magnitude of work on the crate
Consider all four forces. The normal force does no work at all, since there is no motion in the direction of that force, perpendicular to the ramp. The force of gravity is smaller than the force of friction, since you still need to push the crate to get constant velocity. The force of you pushing is also smaller than the force of friction, since you are moving down a ramp, and are therefore assisted by gravity. Therefore the force doing greatest magnitude of work is the force of friction. Note that, even though the frictional work is negative, it still has the greatest magnitude
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A hockey puck with a mass of 160 g is sliding across an empty ice rink. The coefficient of friction between the hockey puck and the ice is 0. 51. The puck travels 47. 7 m before coasting to a stop. What was the initial velocity of the puck?.
The initial velocity of the hockey puck is obtained as 22 m/s.
What is the frictional force?The frictional force of the hockey puck is the force that causes it to stop. Now;
Ff = μmg
Ff = 0. 51 * 0.16 Kg * 9.8 m/s^2
Ff = 0.8 N
Now;
F = mv^2/2x
Where;
m = mass
v = velocity
x = distance
v =√ 2xF/m
v = √ 2 * 47.7 * 0.8 / 0.16
v = 22 m/s
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At which point is the velocity the greatest? at which points is the velocity 0 m/s? at which point is the acceleration 0 m/s2? at which points is the acceleration the greatest?
As per the image: The velocity is maximum at B. The velocity is O at C and A. The acceleration will be O at B
The acceleration is maximum at C and A.
How can it be said?
Two sketches are shown in the attached image. The first one is based on the principle of energy conservation, and it is simple to understand when the velocity is at its highest and when it will be zero.
The pendulum is at its highest height in points A and C relative to the reference point, giving us the most potential energy. Additionally, all of the potential energy had been converted into kinetic energy by the time the pendulum reached point B, therefore this is where its maximum velocity would be.
The second sketch, which displays a free body diagram of the pendulum when it is producing a theta angle with respect to the vertical plane, is shown for the acceleration analysis. Applying Newton's second law and taking into account the forces acting on the pendulum, we arrive at the equation shown in the picture.
With the knowledge that the equation will be zero (0) when the angle theta is 0, we can see that the acceleration, which has the same direction as the velocity, relies on the sin(theta). It implies that at point B, the acceleration will be 0. and at points Cand A, maximum.
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Which part of a laser printer applies a positive charge to the paper that attracts the toner particles to it
The part of laser printer that applies a positive charge to the paper in order to attract the toner particles is known as transfer roller.
What is a laser printer:
A laser printer is a kind of printer that uses the electrostatic digital printing process to perform printing. It makes use of the static electricity and toner powder in place of liquid ink.
The toner is applied to specific areas which are dependent on the charge difference created or on the static electricity.
Following are the components of a laser printer:
Scanning unit:This unit of a laser printer generally consists of a laser diode, a
scanning motor and a polygon mirror.
It also consists of two-beam alignment lenses.
This unit of laser printer consists of three drums, namely primary
charging roller (PCR), organic photoconductive drum (OPC) , and
image transfer roller (ITR).
The transfer roller is also present at a close vicinity of the
printer's toner cartridge.
Fuser assembly unit:This unit of laser printer consists of a pressure roller and a fuser roller, where the fuser roller assembly consists of a heating
element.
Therefore, the transfer roller unit of a laser printer applies a positive charge to the paper that attracts the toner particles to it.
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If the mass of the earth and all objects on it were suddenly doubled, but the size remained the same, the acceleration due to gravity at the surface would become.
When the mass of Earth doubles, acceleration due to gravity doubles as well.
Acceleration due to gravity
Apply Newton's second law of motion;
F = mg --- (1)
where;
m is mass of the objectg is acceleration due to gravityF = GmM/R² --- (2)
where;
M is mass of EarthR is radius of EarthSolve (1) and (2)
mg = GmM/R²
g = GM/R²
when the mass of Earth doubles, acceleration due to gravity becomes;
g' = G(2M)/R²
g' = 2(GM/R²)
g' = 2g
Thus, when the mass of Earth doubles, acceleration due to gravity doubles as well.
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Consider a circuit with a main wire that branches into two other wires. If the current is 10 A in the main wire and 4 A in one of the branches, how much current is in the other branch
If the primary wire's power is 10 A and one branch's power is 4 A, another branch's power will be 6A.
According to Kirchhoff's current law (KCL), the total current flowing through a parallel route circuit's junction equals the total current flowing away from it.
Provided that one of the two branches through which power exits the intersection has a flow of 4A, and also that the junction's overall flow entering it is 10A, the entire current going the junction should be 10A.
Consequently, the second wire's power may be expressed as;
I = I1+ I2 [ where I= total current (10A);
I1= current in one branch (4A) &
I2= current in another branch]
⇒I2 = I - I1
⇒I2 = 10A - 4A
⇒I2 = 6A
Therefore, it can be concluded that when the primary wire bears 10A power having 4A in one of its branches, another branch carries 6A power.
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