right to left left to right A solenoid 2.5 m long and 30 cm in diameter consists
ID: 1769205 • Letter: R
Question
right to leftleft to right A solenoid 2.5 m long and 30 cm in diameter consists of 4500 turns of wire. A 5 turn coil with negligible resistance is wrapped around the solenoid and connected to a 180 A solenoid 2.5 m long and 30 cm in diame resistor, as shown in Fig. 31-47. The direction of the current in the solenoid is such that the solenoid's magnetic field points to the right. At time t = 0 the solenoid current begins to decay exponentially, being given by I = I0e-t/?, where I0 = 85 A, ? =2.5 s, and t is the time in seconds. A solenoid 2.5 m long and 30 cm in diame Figure 31-47. (a) What is the direction of the current in the resistor as the solenoid current decays? right to leftleft to right (b) What is the value of the resistor current at t = 1.0 s in A? A (c) What is the value of the resistor current at t = 5.0 s in A?Explanation / Answer
a) left to right
b)
let N1 = 5 turns
N2 = 4500 turns
d = 0.3 m ==> r = d/2 = 0.15 m
A = pi*r^2
= 3.14*0.15^2
= 0.07065 m^2
L = 2.5m
induced emf = N1*A*dB/dt
we know, B = mue*N2*I/L
= mue*N2*Io*e^(-t/T)/L
dB/dt = mue*N2*Io*e^(-t/T)/(L*T)
induced emf = N1*A*mue*N2*Io*e^(-t/T)/(L*T)
at t = 1s
induced emf = 5*0.07065*4*pi*10^-7*4500*85*e^(-1/2.5)/(2.5*2.5)
= 1.82*10^-2 volts
i = emf/R
= 1.82*10^-2/180
= 101.1 micro A <<<<<<<<<<<-------Answer
c) at t = 5s
induced emf = 5*0.07065*4*pi*10^-7*4500*85*e^(-5/2.5)/(2.5*2.5)
= 3.676*10^-3 volts
i = emf/R
= 3.676*10^-3/180
= 20.42 micro A <<<<<<<<<<<-------Answer
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