If a = 1.0 cm, b = 3.0 cm, and I = 30 A, what is the magnitude and the direction
ID: 1414545 • Letter: I
Question
If a = 1.0 cm, b = 3.0 cm, and I = 30 A, what is the magnitude and the direction of the magnetic field at point P. Assume that the current elements are infinitely long? (b) What is the magnitude and direction of the magnetic force per unit length on the top wire The maximum voltages across the resistor inductor and capacitor are 10 V, 30 V. respectively. The resistance R of the circuit is 5. The frequency of the source is 60 Hz. (a) Determine the maximum voltage across the source V, (b) Determine the maximum current in the circuit, (c) Determine the impedance of the circuit (d) Determine the inductance and the capacitance of the circuit. (e) determine the phase angle,, of the circuit. (f) determine the maximum voltage across the capacitor + inductor.Explanation / Answer
1)
a)
r = sqrt(a^2+b^2)
r = sqrt(1^2+3^2) = 3.163 cm
tantheta = b/a
theta = 71.6 degrees
magnetic field due top wire Bt = uo*i/(2*pi*r) = 4*pi*10^-7*30/(2*pi*0.03163) = 1.897*10^-4 T
magnetic field due to lower wire Bl = uo*i/(2*pi*r) = 4*pi*10^-7*30/(2*pi*0.03163) = 1.897*10^-4 T
net magnetic field B = 2* 4*pi*10^-7*30/(2*pi*0.03163) = 1.897*10^-4*costheta = 1.897*10^-4*cos71.6 = 5.98*10^-5 T
direction to the left
+++++++++++++++
net magnetic force per unit length F = uo*I*I/(2*pi*2a)
F = 4*pi*10^-7*30*30/(2*pi*2*0.01) = 0.09 N/m
direction upwards
++++++++++
2)
Vmax = sqrt(10^2+(30-20)^2) = 14.14 v
b)
Imax = VR /R = 10/5 = 2 A
c)
Z = Vmax/Imax = 7.07 ohms
(d)
vL = Imax*XL = Imax*2*pi*L
30 = 2*2*pi*60*L
L = 40 mH
Vc = Imax*Xc = Imax/(wc)
Vc = Imax/(2*pi*f*C)
20 = 2/(2*pi*60*C)
C = 2.65*10^-4 F
(e)
phase angle = tan^-1(vR/(VL-vc))
phase angle = tan^-1(10/(30-20)) = 45 degrees
(f)
maximum voltage across capacitor+inductor = 30-20 = 10 v