1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
elena-s [515]
3 years ago
6

A 0.200 H inductor is connected in series with a 88.0 Ω resistor and an ac source. The voltage across the inductor is vL=−(12.0V

)sin[(487rad/s)t].
Required:
a. Derive an expression for the voltage vR across the resistor. Express your answer in terms of the variables L, R, VL (amplitude of the voltage across the inductor), ω, and t .
b. What is vR at 2.00 ms? Express your answer with the appropriate units.
Physics
1 answer:
Step2247 [10]3 years ago
3 0

Answer:

a.  (VL)R/ωL[1 - cos[ωt]]  = (10.84 V)[1 - cos[(487rad/s)t]]

b. 1.084 mV

Explanation:

a. Since it is a series circuit, the current in the inductor is the same as the current in the resistor.

Now, the voltage across the inductor vL = -Ldi/dt.

So, the current, i = -1/L∫vLdt.

Now, vL = −(12.0V)sin[(487rad/s)t] and L = 0.200 H

Substituting these into i, we have

i = -1/L∫vLdt

= -1/0.200H∫[−(12.0V)sin[(487rad/s)t]]dt.

= -[−(12.0V)]/0.200H∫[sin[(487rad/s)t]]dt.

= 60V/H∫[sin[(487rad/s)t]]dt

Integrating i, we have

i = 60V/H ÷ [(487rad/s)[-cos[(487rad/s)t]] + C

at t = 0, i(0) = 0

0 = 60V/H ÷ [(487rad/s)[-cos[(487rad/s)× 0]] + C

0 = 60V/H ÷ [(487rad/s)[-cos[0]] + C

0 = 60V/H ÷ [(487rad/s)[-1]+ C

C = 60V/H ÷ [(487rad/s)

So, i = 60V/H ÷ [(487rad/s)[-cos[(487rad/s)t]] + 60V/H ÷ [(487rad/s)

i =  60V/H ÷ [(487rad/s)[1 - cos[(487rad/s)t]]

i = (0.123A)[1 - cos[(487rad/s)t]] = VL/ωL[1 - cos[ωt]] where ω = 487rad/s and VL = 12.0 V and L = 0.200 H

So, the voltage across the resistor vR = iR where R = resistance of resistor = 88.0 Ω

So, vR = iR = VL/ωL[1 - cos[ωt]] × R = (VL)R/ωL[1 - cos[ωt]]

=  (0.123A)[1 - cos[(487rad/s)t]] × 88.0 Ω

= (10.84 V)[1 - cos[(487rad/s)t]]

b. vR at t = 2.00 ms = 0.002 s

So, vR = (10.84 V)[1 - cos[(487rad/s)(0.002)]]

= (10.84 V)[1 - cos[0.974]]

= (10.84 V)[1 - 0.9999]

= (10.84 V)(0.0001)

= 0.001084

= 1.084 mV

You might be interested in
Jimmy is standing 300 feet away from a rocket that is being shot up into the air away from him at an angle of elevation of 70 de
ira [324]

Answer: Vertical height of rocket is 824.24ft

Explanation: see attachment.

Opp/ Adj = Tan 70°

h/ 300 = Tan 70°

h= 300tan 70°

h = 824.24ft

4 0
3 years ago
The measure of the force with which air molecules push on a surface is called
alex41 [277]
It is called air pressure
7 0
3 years ago
A wave has a wavelength of 7 mm and a frequency of 19 hertz. What is its speed?
ASHA 777 [7]

Speed = (frequency) x (wavelength)

Speed = (19 per second) x (7 mm)

Speed = (19 x 7) (per second · mm)

<em>Speed = 133 mm/sec</em>

or you might want to write  <em>Speed = 0.133 m/s</em> .

4 0
3 years ago
Scuba divers are warned that if they must make a rapid ascent, they should exhale on the way up. If a diver rapidly ascends to t
Whitepunk [10]

Air for a diver comes out of a high pressure tank at - Same- pressure compared to the water around the diver (metered by the regulator).

This means the lungs are inflated with - Highly pressurized- gas.

This does not adversely affect the diver when deep underwater, because the entire environment around the diver is at -Same - pressure.

If the diver suddenly surface, the air in the alveoli in the lungs will still be at - a higher - pressure compared to the air around the diver, which will be at - a lower - pressure.

The gas in the diver's lungs will - expand - and can damage the alveoli.

5 0
3 years ago
How does the motion of the molecules change when you increase the temperature
borishaifa [10]

Answer:

They speed up as temperature increases.

Explanation:

As temperatures increases within a molecule the particles will speed up.

6 0
2 years ago
Other questions:
  • Which of the following is a metal?<br> Calcium (Ca)<br> Iron (Fe)<br> Sodium (Na)<br> all of these
    13·1 answer
  • When temperature decreases but actual water vapor content remains the same, what happens to relative humidity?
    15·2 answers
  • A force does 30000 J of work along a distance of 9.5m. Find the applied force.
    8·1 answer
  • How to create a water ripple experiment
    7·1 answer
  • A ? is a conductor installed on the supply side of a service or separately derived system to ensure the required electrical cond
    12·1 answer
  • If you have a yellow sheet of paper and shine a cyan light what color is the paper
    11·2 answers
  • Faraday's law states that voltage can be changed by moving the coil out of the magnetic field true or false
    5·1 answer
  • Each of 100 identical blocks sitting on a frictionless surface is connected to the next block by a massless string. The first bl
    10·1 answer
  • Two identical blocks are heated to different temperatures. The blocks are placed so that they touch, and heat begins to flow bet
    5·1 answer
  • A basketball player has a 0. 603 probability of making a free throw. if the player shoots 10 free throws, what is the probabilit
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!