How Do You Design a Generator to Match Domestic Voltage Specifications?

[brenton]

hey, i have a physics quiestion which i am stuck on any help would be much appreciated

you are asked to design a generator to produce the same 50Hz, 240V(rms) as found in a domestic voltage outlet

The generator is made of a single flat coilbeing made to rotate in a uniform magnetic field of strength 0.08T. the coil may be of any surface area and have as many turns as you like, provided the area and number are "reasonable" values. the length of the coil is L, its width is W, and it spins at an angular rate (omega)w = 2Pi.50 rads/s

What values would you choose for thr area of the coil, A, and for the number of turns, N, that will provide this emf.

i have never done physics before so i don't even no what to begin...could comeone please run me though how i would attempt it..
thankyou

i no u don't do the problems for me but could u give me a formula i might be able to use or any pointers on how to begin this

 

[geosonel]

hey, i have a physics quiestion which i am stuck on any help would be much appreciated

you are asked to design a generator to produce the same 50Hz, 240V(rms) as found in a domestic voltage outlet

The generator is made of a single flat coilbeing made to rotate in a uniform magnetic field of strength 0.08T. the coil may be of any surface area and have as many turns as you like, provided the area and number are "reasonable" values. the length of the coil is L, its width is W, and it spins at an angular rate (omega)w = 2Pi.50 rads/s

What values would you choose for thr area of the coil, A, and for the number of turns, N, that will provide this emf.

i have never done physics before so i don't even no what to begin...could comeone please run me though how i would attempt it..
thankyou

i no u don't do the problems for me but could u give me a formula i might be able to use or any pointers on how to begin this

an AC electric generator uses electromagnetic induction in a coil (rotating in a magnetic field) which is described by Faraday's Law. briefly, the changing magnetic flux thru a coil being rotated in a magnetic filed induces an AC voltage in the coil. the magnetic flux thru the coil is constantly changing because the coil is constantly rotating in the magnetic field, thereby producing (or "inducing") a continuous AC voltage.

the peak AC voltage produced is described by Faraday's Law:
Peak AC Voltage Magnitude = N*B*A*ω
where N is the number of coil turns, B the magnetic field, A the coil crossection area, and ω the angular rotation rate (in radians/sec).

since your problem requires the "RMS" AC Voltage, we divide the above formula by √2=1.414:
RMS AC Voltage Magnitude = N*B*A*ω/1.414

now place the problem's known values into the above equation and solve for (N*A) since the latter will provide your "design" parameters:
(240 volts) = N*(0.08 T)*A*(2*π*50 rads/s)/1.414
(N*A) = (1.414)*(240)/(0.08*2*π*50) = X ? calculate this numerical value

compute the value of X in the above formula.

then to complete the problem, design your generator coil by choosing reasonable values for the number of coil turns (N) and coil crossection area (A in square meters) such that (N*A)=X from the above formula.

 

[thepatientmental]

Sure, I'd be happy to help guide you through this problem. First, let's break down the problem and identify what information we have and what we need to find.

Information:
- We need to design a generator to produce 50Hz, 240V(rms)
- The generator consists of a single flat coil rotating in a magnetic field of 0.08T
- The coil can have any surface area and number of turns, as long as they are reasonable values
- The length of the coil is L, the width is W, and it spins at an angular rate (omega)w = 2Pi.50 rads/s

What we need to find:
- The values for the area of the coil, A, and the number of turns, N, that will produce the desired emf.

To begin, we need to understand the relationship between magnetic field, velocity, and voltage. This is described by Faraday's law of induction, which states that the induced emf in a wire is equal to the rate of change of magnetic flux through the wire.

In simpler terms, this means that the faster the coil rotates in the magnetic field, the higher the induced emf will be. So, the first step would be to calculate the emf needed to produce 240V(rms) at 50Hz.

We can use the formula for rms voltage: V(rms) = V(max) / sqrt(2) = 240 / sqrt(2) = 169.7V.

Next, we need to find the rate of change of magnetic flux through the coil. This can be calculated using the formula: Emf = -N * A * (dΦ/dt), where N is the number of turns, A is the area of the coil, and (dΦ/dt) is the rate of change of magnetic flux.

Since we know the frequency (50Hz), we can calculate the time period (T) using the formula: T = 1 / f = 1 / 50 = 0.02 seconds.

Now, we can plug in the values we know and solve for the remaining variables:
169.7 = -N * A * (dΦ/dt)
169.7 = -N * A * (Φ / T)

We can rearrange this equation to solve for A:
A = - (169.7 * T) / (N * Φ)