Two different questions, show your work. A magnetic field oscillates according t

Question

Two different questions, show your work.

A magnetic field oscillates according to the equation B = 0.02 cos(omega t) in Tesla, where omega is 6rads/sec. If a 245 turn coil of radius 0.10 m, is placed with the plane of the coil to the direction of the magnetic field (max flux) what is (a) the max Emf available? (b) If the coil has a total resistance of 4.0Ohm, what is the current at 1.5s? Given : oscillating voltage applied to an LRC circuit, V = 110cos(120pit), R = 1kOhm, L = 10mH, C = 4700muF. Find (a) the rms voltage, (b) the impedance Z, (c) the rms current, (d) the phasor angle, (e) the resonance frequency.

Explanation / Answer

1)

Bmax=0.02 T

A=pir^2= pi*0.1^2 =0.0314 m^2

a)

Emax= NBAW =0.02*245*6*0.0314

Emax=0.9236 V

b)

E=0.9236cos(Wt)

W=6 rad/s *(180/pi) =343.77 degrees

at t=1.5 s

E=0.9236cos(343.77*1.5)

E=-0.8415 V

I =E/R =0.21 A

2)

a)

Vmax =110 V

Vrms =Vmax/sqrrt(2) =110/sqrt(2

Vrms =77.78 V

b)

W=120pi

XL=WL=120pi*10*10^-3 =3.77 ohms

Xc=1/WC =1/120pi*4700*10^-6

Xc =0.56 ohms

X=XL-XC=3.2 ohms

Z=sqrt(R^2+X^2) =sqrt(1000^2+3.2^2)

Z=1000.005 ohms or 1K ohms

c)

Irms =Vrms/Z =77.78/1000.005

Irms =0.0778 A or 77.8 mA

d)

phi=tan^-1(X/R) =(3.2/1000)

phi=0.1836 degrees

e)

f=1/2pisqrt(LC)=1/2pisqrt(10*10^-3*4700*10^-6)

f=4612.7 Hz or 4.6 KHZ

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