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Andrew [12]
2 years ago
14

The length of an aluminum wire is quadrupled and the radius is doubled. By which factor does the resistance change?

Physics
1 answer:
erik [133]2 years ago
7 0
The resistance of a conductive wire is given by:
R= \frac{\rho L}{A}
where
\rho is the material resistivity
L is the wire length
A is the cross-sectional area of the wire

The length of the wire is quadrupled, so if we call L the original length and L' the new length, we can write 
L'=4 L

Similarly, the radius of the wire is doubled (r'=2r), so the new area is
A'= \pi (r')^2 = \pi (2r)^2 = 4 \pi r^2 = 4A

And if we substitute into the equation, we find that the new resistance of the wire is
R'= \frac{\rho L'}{A'}= \frac{\rho (4L)}{4 A'}  =  \frac{\rho L}{A}=R
Therefore, R=R': this means that the resistance of the wire did not change.
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Using Gauss's law, calculate the electric field at a point distance s from a long wire bearing uniform charge density. i need he
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Answer:

E = 2k  \frac{\lambda}{ r}

Explanation:

Gauss's law states that the electric flux equals the wax charge between the dielectric permeability.

We must define a Gaussian surface that takes advantage of the symmetry of the problem, let's use a cylinder with the faces perpendicular to the line of charge. Therefore the angle between the cylinder side area has the same direction of the electric field which is radial.

            Ф = ∫ E . dA = E ∫ dA = q_{int} /ε₀

tells us that the linear charge density is

            λ = q_ {int} /l

            q_ {int} = l λ

we substitute

            E A = l λ /ε₀

is area of ​​cylinder is

           A = 2π r l

we substitute

            E = \frac{ l \ \lambda}{ \epsilon_o \ 2\pi  \ r \ l }

             E = \frac{\lambda}{ 2\pi  \epsilon_o \ r}

the amount

            k = 1 / 4πε₀

            E = 2k  \frac{\lambda}{ r}

5 0
2 years ago
A 125kg bumper car going 18.5 m/a bumps a 187.kkg bumper car at rest. if the first car (125kg) bounces back at 8 m/s what is the
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3 0
3 years ago
Which scientist is often called the “father of the atomic bomb” because of his work as the head of the manhattan project?
kirza4 [7]

Answer:

J. Robert Oppenheimer

Explanation:

He led the Manhattan project and created the first nuclear bomb in WWII

8 0
3 years ago
A rocket moves upward, starting from rest with an acceleration of +29.4 for 3.98 s. it runs out of fuel at the end of the 3.98 s
topjm [15]
U = 0, initial upward speed
a = 29.4 m/s², acceleration up to 3.98 s
a = -9.8 m/s², acceleration after 3.98s

Let h₁ =  the height at time t, for t ≤ 3.98 s
Let h₂ =  the height at time t > 3.98 s

Motion for  t ≤ 3.98 s:
h₁ = (1/2)*(29.4 m/s²)*(3.98 s)² = 232.854 m
Calculate the upward velocity at t = 3.98 s
v₁ = (29.4 m/s²)*(3.98 s) = 117.012 m/s

Motion for t  > 3.98 s
At maximum height, the upward velocity is zero.
Calculate the extra distance traveled before the velocity is zero.
(117.012 m/s)² + 2*(-9.8 m/s²)*(h₂ m) = 0
h₂ = 698.562 m

The total height is
h₁ + h₂ = 232.854 + 698.562 = 931.416 m

Answer: 931.4 m (nearest tenth)

6 0
3 years ago
Read 2 more answers
A sample of ore containing radioactive strontium 38Sr90 has an activity of 8.2 × 105 Bq. The atomic mass of strontium is 89.908
ahrayia [7]

From the activity values and the decay constant, the mass of of Strontium in the sample is:

1.62 × 10^{-7}g

<h3>What is the decay constant of an element?</h3>

The decay constant of an element is the probability of decay of a nucleus per unit time.

{λ = ln 2 / t1/2 

where;

t1/2 is the half-life of the isotope.

The half-life is converted to seconds since the decay constant is asked in per seconds.

28.8 years = 28.8 × 3.156 × 10^{7} = 908928000 s \\

Hence;

λ = \frac{ln2}{90892800s} = 7.626 s^{-1}

                                       

The activity of the element, A, the decay constant, λ and the number of nuclei, N are related as follows:

  • A = (–) λN

N = \frac{8.25 ×10^{5}}{7.626×10^{-10}} = 1.082 × 10^{15}              

Molar mass of Strontium-90 is 90 g.

1 mole of Strontium-90 contains 6.02×10^23 nuclei.

The mass, m of Strontium in the sample is calculated:

m = 1.082 × 10^{15} × \frac{90 g}{6.02 × 10^{23}} = 1.62 × 10^{-7}g \\

Therefore, the mass of of Strontium in the sample is:

1.62 × 10^{-7} \: g

Learn more about decay constant at: brainly.com/question/17159453

5 0
2 years ago
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