Question

a) A simple generator has a square armature 5.0 cm on a side. The armature has 95 turns of 0.59-mm-diameter copper wire and rotates in a 0.650-T magnetic field. The generator is used to power a lightbulb rated at 12.0 V and 25.0 W. At what rate should the generator rotate to provide 12.0 V to the bulb? Consider the resistance of the wire on the armature.

b) Two resistanceless rails rest 23 cm apart on a 6.0∘ ramp. They are joined at the bottom by a 0.50 Ω resistor. At the top a copper bar of mass 0.030 kg (ignore its resistance) is laid across the rails. The whole apparatus is immersed in a vertical 0.85 T field. What is the terminal (steady) velocity of the bar as it slides frictionlessly down the rails?

c) Design a dc transmission line that can transmit 975 MW of electricity 245 km with only a 2.5% loss. The wires are to be made of aluminum and the voltage is 680 kV . The resistivity of aluminum is 2.65×10−8Ω⋅m. What should be the minimum transmission line diameter.

Answer 1

ONE QUESTION AT A TIME as per the policy

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(a)

First, we find the resistance

R = pL / A

we have four sides of square

R = 1.68e-8 * 95 * 4 * 0.05 / pi * 0.295e-3²

R = 1.1675 ohms

and

Irms = 25 / 12 = 2.083 A

so,

Emf = 12 + 2.083 * 1.1675

Emf = 14.4319 V

so,

2$\pi$fNBA / sqrt ( 2) = 14.4319

f = 20.41 / 2$\pi$NBA

f = 20.41 / 2$\pi$ * 95 * 0.65 * 0.05²

f = 21 Hz