The answers are as follows;
a) the inductive reactance is 322 ohm
b) The maximum voltage is 387.5 V
c) The rms and maximum currents in the inductor are 1.2 A and 0.85 A.
<h3>What is the reactance?</h3>
The reactance is obtained from;
XL = 2πfL
XL = 2 * 3.14 * 57.0 * 0.900
XL = 322 ohm
The maximum voltage is obtained as;
Vo = Vrms * √2
Vo = 274 V * √2
Vo = 387.5 V
Io = Vo/XL
Io = 387.5 V/ 322 ohm
Io = 1.2 A
Irms = 274 V/322 ohm
Irms = 0.85 A
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The mass on the left has a downslope weight of
W1 = 3.5kg * 9.8m/s² * sin35º = 19.7 N
The mass on the right has a downslope weight of
W2 = 8kg * 9.8m/s² * sin35º = 45.0 N
The net is 25.3 N pulling downslope to the right.
(a) Therefore we need 25.3 N of friction force.
Ff = 25.3 N = µ(m1 + m2)gcosΘ = µ * 11.5kg * 9.8m/s² * cos35º
25.3N = µ * 92.3 N
µ = 0.274
(b) total mass is 11.5 kg, and the net force is 25.3 N, so
acceleration a = F / m = 25.3N / 11.5kg = 2.2 m/s²
tension T = 8kg * (9.8sin35 - 2.2)m/s² = 27 N
Check: T = 3.5kg * (9.8sin35 + 2.2)m/s² = 27 N √
hope this helps. :)
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