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3 years ago

In order to add or subtract numbers in scientific notation do the exponents have to be the same

1 answer:

3 0

Yes they do. So if you need to add or subtract a pair, then you have to first change one or the other so that they both have the same power of 10.

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An alternator consists of a coil of area A with N turns that rotates in a uniform field B around a diameter perpendicular to the

svet-max [94.6K]

Answer:

(a): emf = $\rm 2\pi f NBA\sin(2\pi ft).$

(b): Amplitude of alternating voltage = 20.942 Volts.

Explanation:

<u>Given:</u>

Area of the coil = A.
Number of turns of coil = N.
Magnetic field = B
Rotation frequency = f.

(a):

The magnetic flux through the coil is given by

$\phi = \vec B \cdot \vec A=BA\cos\theta$

where,

$\vec A$ = area vector of the coil directed along the normal to the plane of the coil.

$\theta$ = angle between $\vec B$ and $\vec A$ .

Assuming, the direction of magnetic field is along the normal to the plane of the coil initially.

At any time t, the angle which magnetic field makes with the normal to the plane of the coil is $2\pi ft$

Therefore, the magnetic flux linked with the coil at any time t is given by

$\phi(t) = NBA\cos(2\pi ft)$

According to Faraday's law of electromagnetic induction, the emf induced in the coil is given by

$e=-\dfrac{d\phi}{dt}\\=-\dfrac{d(NBA\cos(2\pi ft))}{dt}\\=-NBA(-2\pi f\sin(2\pi ft))\\=2\pi f NBA\sin(2\pi ft).$

(b):

The amplitude of the alternating voltage is the maximum value of the emf and emf is maximum when $\sin(2\pi ft)=1.$

Therefore, the amplitude of the alternating voltage is given by

$e_o = 2\pi ft NBA.$

We have,

$N=100\\A=10^{-2}\ m^2\\B=0.1\ T\\f=2000\ rev/ min = 2000\times \dfrac{1}{60}\ rev/sec=33.33\ rev/sec.$

Putting all these values,

$e_o = 2\pi \times 33.33\times 100\times 0.1\times 10^{-2}=20.942\ Volts.$

7 0

3 years ago

A baseball pitcher throws a ball at 97.0 mi/h in the horizontal direction. How far does the ball fall vertically by the time it

mario62 [17]

Answer:

Explanation:

1 mile=5280 ft

1 hour=3600 seconds

Changing speed from mi/h to ft/s

$97 mi/h \times \frac {5280}{3600}=142.2666667 ft/s\approx 142.27 ft/s$

Time of flight, $t=\frac {distance}{speed}=\frac {60.5}{142.27}=0.425257732 s\approx 0.425 s$

From fundamental kinematics equations

$h=0.5gt^{2}$ where g is acceleration due to gravity whose value is taken as 32.2 ft/s2 and h is the distance

By substitution

$h=0.5\times 32.2\times 0.425^{2}=2.9080625 m\approx 2.91 m$

7 0

3 years ago

What is the change in air pressure over a given distance called?.

emmainna [20.7K]

The change in pressure measured across a given distance called a Pressure Gradient. The pressure gradient creates a net force that is directed from higher to lower pressure and is called the Pressure Gradient Force. ... As air increases in velocity, it is deflected by the Coriolis Force.

5 0

2 years ago

**URGENT** Roberto plans to use two transformers to reduce a voltage of 120 V to 4 V. He uses a transformer that has 300 coils i

skelet666 [1.2K]

As we know that in transformers we have

$\frac{V_s}{V_p} = \frac{N_s}{N_p}$

here we know that

$V_s = 4 Volts$

$V_p = 120 Volts$

$N_s = 50 coils$

$N_p = 300 coils$

now from above equation we will have

$\frac{V}{120} = \frac{50}{300}$

$V = 20 Volts$

now we have to reduce this voltage to final voltage of V = 4 V

so again we will have

$\frac{V_s}{V_p} = \frac{N_s}{N_p}$

$\frac{4}{20} = \frac{N_s}{N_p}$

$\frac{N_s}{N_p} = \frac{1}{5}$

so we need to take such a winding whose ratio is 1:5

So it is satisfied in X

$N_p = 60$

$N_s = 12$

so answer will be

3 0

2 years ago

Read 2 more answers

A football is kicked at ground level with the speed of 32 m/s at an angle of 40 degrees to the horizontal. how much later does i

LUCKY_DIMON [66]

the question was a football is kicked at ground level with a speed of 32 m/s the an angle of 40 degrees to the horizontal how much later does it hit the ground probably like 30 more or 40 sense it was around 32

4 0

3 years ago