Please show work and formulas used. Thanks. Please help. 1. I have a weak cerami
ID: 3894452 • Letter: P
Question
Please show work and formulas used. Thanks. Please help.
1. I have a weak ceramic disk magnet (0.125T, 59mm diameter) that can flip even when inside the big solenoid, to make it into a generator.
a) calculate the disk magnet's magnetic flux
b) at what angular speed does the disk need to be flipped, to generate 12V peak?
c) a 220?F Capacitor is going to be connected; what is its Capacitative Reactance at that angular speed?
d) calculate the peak Current and the peak Power into the capacitor, when connected to the 12Vp generator.
2. Suppose we connect the little 90mH solenoid in series with the 220?F capacitor, powered by a 12V (peak) generator at 20Hz.
a) compute the Resistive, Capacitative, and Inductive Reactances of the series devices, individually.
b) compute the total Impedance of all series devices, and the current thru them ; does the current lead, or lag, the voltage?
c) repeat (a) and (b) for a 60Hz frequency
d) repeat for their resonance frequency ... why is the current not infinite, at this resonance frequency?
Explanation / Answer
1.
Area
A=pi*d^2/4 =pi*(59*10^-3)^2/4
A=2.734*10^-3 m^2
a)
flux
phi=BA =0.125*2.734*10^-3
phi =3.42*10^-4 Wb
b)
E=NBAW
W=E/NBA =12/3.42*10^-4
W=35,113.76 rad/s
c)
Xc=1/WC =1/35113.76*220*10^-6
Xc=0.1294 ohms
d)
Ip=V/Xc=12/0.1294 =92.7 A
P=Ip^2*Xc =92.7^2*0.1294
P=1111.98 Watts =1112 W approx
2)
a)
Resitive component
R=0 ohms
XL=2pifL=2pi*20*90*10^-3
XL=11.31 ohms
Xc=1/2pifC=1/2pi*20*220*10^-6
Xc=36.17 ohms
b)
impedance
Z=sqrt[(Xl-Xc)^2]=sqrt[(11.31-36.17)^2]
Z=24.86 ohms
Maximum current
Ip=V/Z=12/24.86
Ip=0.4827 A
c)
at f=60 Hz
XL=2pi*60*90*10^-3=33.93 ohms
Xc=1/2pi*60*220*10^-6= 12.06 ohms
Z=sqrt[33.93-12.06)^2]=21.87
Ip=12/21.87=0.5487 A
d)
resonant frequency
f=1/2pisqrt(LC) =1/2pi*sqrt(90*10^-3*220*10^-6)
f=35.77 Hz
XL=2pi*35.77*90*10^-3=20.23 ohms
Xc=1/2pi*35.77*220*10^-6=20.23 ohms
since XL=Xc
Z=sqrt[(20.23-20.23)^2]=0 ohms
so
Ip=V/Z =12/0 =infinity