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vagabundo [1.1K]
3 years ago
13

: Suppose somebody, using the same apparatus which you used, measured I = 45.5 ma, and V = 8.2 volts on some resistor. Using you

r recorded uncertainties for the 50 ma and 10-volt scales, what would be the maximum % uncertainty in R if it were calculated from the Ohm’s Law Equation (1)? Use calculus methods to answer this question if you can.
Physics
1 answer:
Alex3 years ago
8 0

Answer:

R = (18 ± 2) 10¹ Ω

ΔR = 2 10¹ Ω

Explanation:

Ohm's law relates voltage to current and resistance

           V = i R

            R = \frac{V}{i}V / i

the absolute error of the resistance is

           ΔR = | | \frac{dR}{DV} | \ \Delta V + | \frac{dR}{di} | \ \Delta i

the absolute value guarantees the worst case, maximum error

           ΔR = \frac{1}{i} \Delta V+ \frac{V}{i^2} \Delta i

The error in the voltage let be approximate, if we use a scale of 10 V, in general the scales are divided into 20 divisions, the error is the reading of 1 division, let's use a rule of direct proportion

          ΔV = 1 division = 10 V / 20 divisions

          ΔV = 0.5 V

The current error must also be approximate, if we have the same number of divisions

           Δi = 50 mA / 20 divisions

           Δi = 2.5 mA

       

let's calculate

          ΔR = \frac{1}{45.5 \ 10^{-3}} \ 0.5 + \frac{8.2}{(45.5 \ 10^{-3})^2 } \ 2.5 \ 10^{-3}

          ΔR = 10.99 + 9.9

          ΔR = 20.9 Ω

The absolute error must be given with a significant figure

          ΔR = 2 10¹ Ω

the resistance value is

          R = 8.2 / 45.5 10-3

          R = 180 Ω

the result should be

          R = (18 ± 2) 10¹ Ω

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Consider a transformer. used to recharge rechargeable flashlight batteries, that has 500 turns in its primary coil, 3 turns in i
Rashid [163]

Answer:

<em>a) 0.72 V</em>

<em>b) 19.2 mA</em>

<em>c) 2.304 Watts</em>

Explanation:

A transformer is used to step-up or step-down voltage and current. It uses the principle of electromagnetic induction. When the primary coil is greater than the secondary coil, the it is a step-down transformer, and when the primary coil is less than the secondary coil, the it is a step-up transformer.

number of primary turns = N_{p} = 500 turns

input voltage = V_{p} = 120 V

number of secondary turns = N_{s} = 3 turns

output voltage = V_{s} = ?

using the equation for a transformer

\frac{V_{s} }{V_{p} }  = \frac{N_{s} }{N_{p} }

substituting values, we have

\frac{V_{s} }{120 }  = \frac{3 }{500} }

500V_{p}  = 120*3\\500V_{p} = 360

V_{p} = 360/500 =<em> 0.72 V</em>

<em></em>

b) by law of energy conservation,

I_{P}V_{p} = I_{s}V_{s}

where

I_{p} = input current = ?

I_{s} = output voltage = 3.2 A

V_{s} = output voltage = 0.72 V

V_{p} = input voltage = 120 V

substituting values, we have

120I_{p} = 3.2 x 0.72

120I_{p} = 2.304

I_{p}  = 2.304/120 = 0.0192 A

= <em>19.2 mA</em>

<em></em>

c) power input = I_{p} V_{p}

==> 0.0192 x 120 = <em>2.304 Watts</em>

7 0
3 years ago
A -0.06 charge that moves downward is in a uniform electric field with a strengthened of 200 N/C. What is the magnitude and dire
Nookie1986 [14]

Answer:

The magnitude of the force is 12 N Upwards

Explanation:

The force on a positive charge will be in the same direction as the field, but the force on a negative charge will be in the opposite direction to the field. Thus the direction of the force is upward.

Given;

magnitude of charge, q = 0.06 C

magnitude of electric field, E = 200 N/C

The magnitude of the force is given by;

F = qE

F = 0.06 x 200 N/C

F = 12 N Upwards

Therefore, the magnitude of the force is 12 N Upwards

5 0
3 years ago
A 5.00-m-long uniform ladder, weighing 200 N, rests against a smooth vertical wall with its base on a horizontal rough floor, a
Morgarella [4.7K]

Answer:

0.488  m  

Explanation:

If θ be the angle ladder makes with the plane

cos θ = 1.2 / 5

Tan θ = 4.04

Let the height a person of weight 600 N  can climb be h from the ground .

Distance from the base point  where ladder touches the floor  = h / tanθ

= h / 4.04

Total reaction force = total downward force

R = 200 + 600

800 N

Frictional force = μ R

= .2 x 800

= 160 N

Taking moment of force about the point on the ladder  where it  touches the floor  and balancing them

200 x 1.2 x .5 + 600 x   h / tanθ  = μ R x  1.2 / tanθ ( reaction  at the top point of ladder where it touches the wall is  R₁ and

R₁ =μ R   )

= 200 x 1.2 x .5 + 600 x   h / tanθ  = 160 x 1.2 / tanθ

120  - 600 h / 4.04 = 47.52

120 - 47.52 = 600 h / 4.04

72.48= 148.51 h

h = 0.488  m  

=

5 0
3 years ago
A cyclist is taking part in the Tour de France, which is a bicycle race that takes place every year.
marishachu [46]
Solve the following word problems.
1. The ratio of red marbles and blue marbles that Carlo has is 8: 3. When he
exchanged 35 red marbles for 20 blue marbles from his brother, he was left with
equal number of red and blue marbles.
How many red and blue marbles did he have at the beginning
How many red and blue marbles did he have now
5 0
2 years ago
A proton traveling to the right enters a region of uniform magnetic field that points into the screen. When the proton enters th
muminat

Answer:

deflected toward bottom of the screen

Explanation:

When entering the region with magnetic field, a magnetic force is exerted on the proton. This force is perpendicular to both the direction of the magnetic field and the direction of the velocity of the proton.

The direction of the force can be determined by using the right-hand rule. We have:

- Index finger: direction of the velocity of the proton --> to the right

- Middle finger: direction of the magnetic field --> into the screen

- Thumb: direction of the magnetic force --> toward bottom of the screen

So, the correct answer is

deflected toward bottom of the screen

8 0
3 years ago
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