Question

3) The magnetic field between the poles of an electromagnet is increasing at a rate of 0.04T/s (see fig. 4). The area of the conducting loop in the field is 100 cm², and the total circuit resistance, including the meter, is 42. Find the induced emf and the induced current in the circuit. South B 120 S -1 North Fig. 4. Magnetic field in an electromagnet 4) a) Find the angular frequency of underdamped oscillations in an L-R-C series circuit with inductance 2H, resistance 2012 and capacitance 10mF. b) Find the turn ratio in a transformer if the ratio of effective resistances in primary and secondary coil is 16.

Answer 1

3)induced emf e=d$\Phi$/dt

$\Phi$=magnetic flux=BAcos$\Theta$

B=magnetic field

A=area of loop=100cm2=100xm2

10

$\Theta$=angle between B and normal(perpendicular) to loop=20

$\Phi$=Bx100x
10
xcos20=0.94x
10-2
B

induced emf e=d$\Phi$/d=d(0.94x
10-2
B)/dt=0.94x
10-2
dB/dt

dB/dt=0.04T/s

e=0.94x
10-2
x0.04=3.76x
10
volt

induced current i=e/R=3.76x
10
/4=9.4x$10^{-5}$A (R=resistance=4$\Omega$)

4)a)Angular frequency =1/$\sqrt{LC}$

L=inductance=2H

C=capacitance=10mF=0.01F

Angular frequency =1/$\sqrt{LC}$=1/$\sqrt{2X0.01}$=7rad/sec

b)R1/R2=(V1/I1)x(V2/I2)=V1xI2/V2xI1

R=resistance

V=voltage

I=current

1 for primary and 2 for secondary

For transformer V1/V2=I2/I1=n1/n2=n

n1/n2=n=turn ratio

Hence R1/R2=V1xI2/V2xI1=$n^{2}$

R1/R2=16(given)

16=$n^{2}$

n=$\sqrt{16}$=4=turn ratio