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Arlecino [84]
3 years ago
5

An external resistor with resistance R is connected to a battery that has emf ε and internal resistance r. Let P be the electric

al power output of the source. By conservation of energy, P is equal to the power consumed by R. What is the value of P in the limit that R is:_______. (a) What is the value of P in the limit that R is very small?
(b) What is the value of P in the limit that R is very large?(c) Show that the power output of the battery is a maximum when R = r . What is this maximum P in terms of ε and r? (d) A battery has [Math Processing Error] and [Math Processing Error]. What is the power output of this battery when it is connected to a resistor R, for [Math Processing Error], [Math Processing Error], and [Math Processing Error]? Are your results consistent with the general result that you derived in part (b)?
Physics
1 answer:
ELEN [110]3 years ago
8 0

Answer:

a. 0 W b. ε²/R c. at R = r maximum power = ε²/4r d. For R = 2.00 Ω, P = 227.56 W. For R = 4.00 Ω, P = 256 W. For R = 6.00 Ω, P = 245.76 W

Explanation:

Here is the complete question

An external resistor with resistance R is connected to a battery that has emf ε and internal resistance r. Let P be the electrical power output of the source. By conservation of energy, P is equal to the power consumed by R. What is the value of P in the limit that R is (a) very small; (b) very large? (c) Show that the power output of the battery is a maximum when R = r . What is this maximum P in terms of ε and r? (d) A battery has ε= 64.0 V and r=4.00Ω. What is the power output of this battery when it is connected to a resistor R, for R=2.00Ω, R=4.00Ω, and R=6.00Ω? Are your results consistent with the general result that you derived in part (b)?

Solution

The power P consumed by external resistor R is P = I²R since current, I = ε/(R + r), and ε = e.m.f and r = internal resistance

P = ε²R/(R + r)²

a. when R is very small , R = 0 and P = ε²R/(R + r)² = ε² × 0/(0 + r)² = 0/r² = 0

b. When R is large, R >> r and R + r ⇒ R.

So, P = ε²R/(R + r)² = ε²R/R² = ε²/R

c. For maximum output, we differentiate P with respect to R

So dP/dR = d[ε²R/(R + r)²]/dr = -2ε²R/(R + r)³ + ε²/(R + r)². We then equate the expression to zero

dP/dR = 0

-2ε²R/(R + r)³ + ε²/(R + r)² = 0

-2ε²R/(R + r)³ =  -ε²/(R + r)²

cancelling out the common variables

2R =  R + r

2R - R = R = r

So for maximum power, R = r

So when R = r, P = ε²R/(R + r)² = ε²r/(r + r)² = ε²r/(2r)² = ε²/4r

d. ε = 64.0 V, r = 4.00 Ω

when R = 2.00 Ω, P = ε²R/(R + r)² = 64² × 2/(2 + 4)² = 227.56 W

when R = 4.00 Ω, P = ε²R/(R + r)² = 64² × 4/(4 + 4)² = 256 W

when R = 6.00 Ω, P = ε²R/(R + r)² = 64² × 6/(6 + 4)² = 245.76 W

The results are consistent with the results in part b

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borishaifa [10]

Answer and Explanation:

If the ant was to crawl 50cm to the right, then come back 30 cm, then the total distance walked would be <u>80cm</u>.

- Combine 50cm and 30cm to get 80 cm.

For displacement, the answer is <u>20 cm.</u>

- When calculating displacement, you use the initial (starting) distance. and subtract that from the final distance, giving you the displacement, or the amount traveled from the starting point to the final point if you were to make a straight line from the starting point to end point. (0 to 50, then back 30 the same direction, so subtract 30 from 50 to get 20)

<em><u>#teamtrees #PAW (Plant And Water)</u></em>

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8 0
2 years ago
Read 2 more answers
PHYSICS PLEASE HELP
vaieri [72.5K]

1.)Answer:

The correct answer is C.

Explanation:

Displacement is a vector quantity so it may be either positive or negative. As per convention, acceleration taken as positive when moves downward direction. But, in our case, acceleration towards downward taken as negative, so displacement should also be negative because negative sign only indicate its downward direction.

2.) Answer

The correct answer is C. The time won't change, but horizontal distance will double.

Explanation:

First case

velocity = v = 20 m/s

Height = h = 10 m

We need to calculate time (t) and horizontal distance (x)

using 2nd equation of motion

h = vt + 0.5 gt²

As initial vertical velocity is 0. So

h = 0.5(9.8)t²

It can be see that time does not depends on initial velocity, so it won't change

to calculate x

x = vt

It can be see that horizontal distance will double because depends on velocity.

3.)Question

Illustration:

Day 1: 10 km west and spent night at A.

Day 2: 10 km west and night in a tent B.

Day 3: 20 km west and then they turned around and went back to the home because Jerry left his allergy medicine.

Day 4: 30 km North to the point D.

Answer

The correct answer is C.

Explanation:

On Day 1, Day 2 and Day 3, they move towards west 40 km from home and then turned back to home because Jerry forget his medicine. Thus the total distance is 80 km but the displacement is zero because displacement is the measure from initial to final position. As initial and final position is same at the end of 3rd day so displacement is zero. Fourth day, They move towards north 30 km and hence total distance is 110 km. And total displacement is only 30 km.

4.) Answer:

The correct Answer is A.

Explanation:

To calculate horizontal distance (x), we only need to find the horizontal component of velocity that is

vₓ = v Cos (70°)

vₓ = 41 m/s

As we know that x = vₓ t

So,

x = 41t

5.) Answer

The correct Answer is B.

Explanation:

Displacement is a vector quantity so it depends on direction. As Sally moves 10m forward and then 5m backward, So his total displacement is 5m. While the distance is scalar quantity independent of direction. So the total distance covered by Sally is 15m which is 10m greater than the displacement.  

6.)Answer

The correct answer is A.

Explanation:

Consider

horizontal(h)= 6m

vertical = Xm

Hypotenuse(H) = ?

Angle = 37°

As we know that

H×Cos∅ = h

So,

H = h ÷ Cos(∅)

  = 6 ÷ Cos(37)

H = 7.5 m    

7.) Answer:

The correct answer is D.

Explanation:

In projectile motion, horizontal distance depends on initial velocity and angle with ground. So as the player increase the velocity of the ball, more distance will be covered. As far as he increase the angle upto 45° with the ground, the horizontal distance will increase. That's why the player should increase the ball's initial velocity and kick it at a 45° angle.

8.)Answer:

The correct Answer is B.

Explanation:

Consider

Vector A  = 3m

Vector B  = 4m

Angle = ?

As the angle ∅ is created between vectors C and A.

we know that

tan∅ = vertical ÷ horizontal

tan∅ = 4 ÷ 3

∅ = tan⁻¹ (1.33)

∅ = 53.1°

9.) Answer:

The correct Answer is C.

Explanation:

Projectile motion depends on initial velocity and initial angle with ground. As far as we increase the velocity of the ball, more distance will be covered. As it also depends on angle, So as far as we increase the angle up to 45° with the ground, the horizontal distance will increase. But when the angle is above 45°, increasing angle decrease the horizontal distance.

10.) Answer:

The correct Answer is B.

Explanation:

Given data :

∅ = 20°

initial velocity = 40 m/s

As we need to find the vertical component of velocity

So, initial upward velocity = initial velocity × Sin∅ = 40 × Sin 20°

             initial upward velocity = 13.68 m/s

11.)Answer:

The correct Answer is B.

Explanation:

The projectile motion depends on the angle with the horizontal.As far as we increase the angle up to 45° with the ground, the distance will increase. But when the angle is above 45°, increasing angle decrease the horizontal distance.

12.) Answer:

The correct answer is D.

Explanation:

Given data

Initial speed = V₀ =40 m/s

angle = 60°

g = 9.81 m/s²

First we need to find initial vertical velocity (V)

V = V₀ Sin∅

V = 34.64 m/s

3rd equation of motion

2gh = V₁² - V²

As we need to find maximum height so at highest point vertical final velocity (V₁) = 0

So,

h = V² ÷ 2g

 = 34.64² ÷ 2×9.81

                              h = 61.2 m

13.) Answer:

The correct answer is C.

Explanation:

A bird flying in the air is 3D motion as the bird move up, down, right, left all the possible direction. A leaf falling from a tree is also a 3D motion because a leaf never fall in absolute vertical manner. A lady bug crawling on a soccer ball also 3D. If lady bug crawling on a plane like floor then it is 2D but now lady bug crawling on soccer ball which is in spherical shape so it is also 3D motion. Only train travelling along a track is 2D because train cannot move up and down and the track of train is in a plane. So it is 2D motion.  

6 0
3 years ago
Read 2 more answers
Two ice skaters, Paula and Ricardo, initially at rest, push off from each other. Ricardo weighs more than Paula.
sveta [45]

Answer:

the two ice skater have the same momentum but the are in different directions.

Paula will have a greater speed than Ricardo after the push-off.

Explanation:

Given that:

Two ice skaters, Paula and Ricardo, initially at rest, push off from each other. Ricardo weighs more than Paula.

A. Which skater, if either, has the greater momentum after the push-off? Explain.

The law of conservation of can be applied here in order to determine the skater that possess a greater momentum after the push -off

The law of conservation of momentum states that the total momentum of two  or more objects acting upon one another will not change, provided there are no external forces acting on them.

So if two objects in motion collide, their total momentum before the collision will be the same as the total momentum after the collision.

Momentum is the product of mass and velocity.

SO, from the information given:

Let represent the mass of Paula with m_{Pa} and its initial velocity with u_{Pa}

Let represent the mass of Ricardo with m_{Ri} and its initial velocity with u_{Ri}

At rest ;

their velocities will be zero, i.e

u_{Pa} = u_{Ri} = 0

The initial momentum for this process can be represented as :

m_{Pa}u_{Pa} +  m_{Ri}u_{Ri} = 0

after push off from each other then their final velocity will be v_{Pa} and v_{Ri}

The we can say their final momentum is:

m_{Pa}v_{Pa} +   m_{Ri}v_{Ri} = 0

Using the law of conservation of momentum as states earlier.

Initial momentum = final momentum = 0

m_{Pa}u_{Pa} +  m_{Ri}u_{Ri} =  m_{Pa}v_{Pa} +   m_{Ri}v_{Ri}

Since the initial velocities are stating at rest then ; u = 0

m_{Pa}(0) + m_{Pa}(0) = m_{Pa}v_{Pa} +   m_{Ri}v_{Ri}

m_{Pa}v_{Pa} +   m_{Ri}v_{Ri}  = 0

m_{Pa}v_{Pa} = - m_{Ri}v_{Ri}

Hence, we can conclude that the two ice skater have the same momentum but the are in different directions.

 B. Which skater, if either, has the greater speed after the push-off? Explain.

Given that Ricardo weighs more than Paula

So m_{Ri} > m_{Pa} ;

Then \mathsf{\dfrac{{m_{Ri}}}{m_{Pa} }= 1}

The magnitude of their momentum which is a product of mass and velocity can now be expressed as:

m_{Pa}v_{Pa} =  m_{Ri}v_{Ri}

The ratio is

\dfrac{v_{Pa}}{v_{Ri}} =\dfrac{m_{Ri}}{m_{Pa}} = 1

v_{Pa} >v_{Ri}

Therefore, Paula will have a greater speed than Ricardo after the push-off.

6 0
3 years ago
The wavelength of the visible line in the hydrogen spectrum that corresponds to m = 5 in the Balmer equation is: A. 656 nm. B. 4
BaLLatris [955]

Answer:

The wavelength of the visible line in the hydrogen spectrum is 434 nm.

Explanation:

It is given that, the wavelength of the visible line in the hydrogen spectrum that corresponds to n₂ = 5 in the Balmer equation.

For Balmer series, the wave number is given by :

\dfrac{1}{\lambda}=R(\dfrac{1}{n_1^2}-\dfrac{1}{n_2^2})

R is the Rydberg's constant

For Balmer series, n₁ = 2. So,

\dfrac{1}{\lambda}=1.097\times 10^7\times (\dfrac{1}{2^2}-\dfrac{1}{5^2})

\lambda=4.34\times 10^{-7}\ m

or

\lambda=434\ nm

So, the wavelength of the visible line in the hydrogen spectrum is 434 nm. Hence, this is the required solution.

6 0
3 years ago
Which of the answer choices is a true statement? Select all that apply. Metallic elements usually exist as molecules, combining
lianna [129]

Metallic elements can exist on their own as individual atoms.

Nonmetals usually exist as molecules, combining with atoms of themselves.

Nonmetals can exist on their own as individual atoms.

Explanation:

Metallic elements can exist on their own as individual atoms. They have a large radius and are stable enough to freely exist as single atoms. The metallic bonding in them gives them stability.  Example Gold, Silver, Platinum e.t.c

Non-metals are usually found in combined as state as molecules. They are usually joined together by covalent attraction. The bonds are formed with the atoms shares their valence electrons and their octet is completed. For example nitrogen gas, oxygen gas.

Most noble gases are non-metals that exist as individual mono-atomic gases on their own. The gases are stable and have an octet/duet configuration. For example helium gas, neon gas e.t.c

learn more;

Metals and non-metals brainly.com/question/2758034

#learnwithBrainly

7 0
3 years ago
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