In Figure 30-37 a 120-turn coil of radius 1.8 cm and resistance 7.0 is coaxial w

Question

In Figure 30-37 a 120-turn coil of radius 1.8 cm and resistance 7.0 is coaxial with a solenoid with 200 turns/cm and diameter 3.2 cm.

(a) The solenoid current drops uniformly from 1.5 A to zero in time interval delta t = 25 ms. What magnitude of current is induced in the coil during delta t?

(b) Suppose instead that the solenoid current drops according to the function i = 1.5 e^(-80 t), where t is in seconds and the current is in A. What is the magnitude of the initial induced current in the coil?

(c) What are the units of the number 80 in the exponential?

s, 1/s, A ,No units

Explanation / Answer

given

N = 120 turns

r = 1.8 cm

R = 7 ohms

n = 200 turns/cm = 20000 turns/m

d = 3.2 cm = 0.032 m

a) magnetic field inside a solenoid, B = mue*n*I

induced emf in the coil = N*A*dB/dt

= N*(pi*d^2/4)*mue*n*dI/dt

= 120*(pi*0.032^2/4)*4*pi*10^-7*20000*(1.5-0)/(25*10^-3)

= 0.146 V

induced current = induced emf/R

= 0.146/7

= 0.0209 A

b) I = 1.5*10^(-80*t)

dI/dt = 1.5*e^(-80*t)*80

= 120*e^(-80*t)

at t = 0,

dI/dt = 120 A/s

so,

inudued emf = N*(pi*d^2/4)*mue*n*dI/dt

= 120*(pi*0.032^2/4)*4*pi*10^-7*20000*120

= 0.291 V

induced current = induced emf/R

= 0.291/7

= 0.0416 A

c) 1/s

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.