The uniform magnetic field strength is 0.15 Tesla. The square coil consists of 2
ID: 1699219 • Letter: T
Question
The uniform magnetic field strength is 0.15 Tesla. The square coil consists of 250 turns and the length of a side of the coil is 90 cm. The rate of rotation is 16 rpm.
a) What is the maximum value of the magnetic flux through the coil?
b) Use the approximation V ave= N /t to approximate the voltage generated. t is the time for a quarter cycle.
c) Write a function for the magnetic flux through the coil as a function of time ( must be in units of radians per second.). Use exact values.
d) Write a function for the induced voltage output from the coil as a function of time.
e) Suppose you wanted to use this generator to supply the electrical needs of a household that needs 3100 Watts of power. (They have special appliances that operate off the frequency and voltage of your generator. You plan to use a waterfall with a drop of 6 m to power the generator. What would the flow rate of the stream have to be in liters/second if the generator were 100% efficient?( 1 L= 1 kg; g=9.8 m/s^2)
f) If the whole generating process were only 60 % efficient, what would the flow rate have to be?
Explanation / Answer
The uniform magnetic field strength is 0.15 Tesla. The square coil consists of 250 turns and the length of a side of the coil is 90 cm. The rate of rotation is 16 rpm. a) What is the maximum value of the magnetic flux through the coil? 0.15*250*90e-2^2=30.4 b) Use the approximation V ave= N ?f/?t to approximate the voltage generated. ?t is the time for a quarter cycle. V ave = N* ?phi/?t = 30.4/(1/16*4)=1950(V) c) Write a function for the magnetic flux through the coil as a function of time (? must be in units of radians per second.). Use exact values. =30.4*cos(wt) where w=1/(16*2pi)=0.01 d) Write a function for the induced voltage output from the coil as a function of time. so U=-30.4*0.01*sin(wt) e) Suppose you wanted to use this generator to supply the electrical needs of a household that needs 3100 Watts of power. (They have special appliances that operate off the frequency and voltage of your generator. You plan to use a waterfall with a drop of 6 m to power the generator. What would the flow rate of the stream have to be in liters/second if the generator were 100% efficient?( 1 L= 1 kg; g=9.8 m/s^2) we have that 3100=F*9.8*6. where F be flow rate. so F=53(kg/s) f) If the whole generating process were only 60 % efficient, what would the flow rate have to be? 3100=F*9.8*6*0.6 so F=88(kg/s)
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