Problem-2: Figure I shows a simple rotating loop between curved pole faces connected to a battery and a resistor through a switch. The resistor shown models the total resistance of the battery and the wire in the machine. The physical dimensions and characteristics of this machine are \[ \begin{array}{rlrl} r & =0.5 \mathrm{~m} & l & =1.0 \mathrm{~m} \\ R & =0.3 \Omega & B & =0.25 \mathrm{~T} \\ V_{\mathrm{b}} & =120 \mathrm{~V} & \end{array} \] (a) What bappens when the switch is closed? (b) What is the machine's maximum starting current? What is its steady-state angular velocity at no load? (c) Suppose a load is attached to the loop, and the resulting ioad lorque is $10 \mathrm{~N} \cdot \mathrm{m}$. What would the new steady-state speed be? How much power is supplied to the shaft of the machine? How much power is being supplied by the battery? Is this machine a motor or a generator? (d) Suppose the machine is again unloaded, and a torque of $7.5 \mathrm{~N} \cdot \mathrm{m}$ is applied to the shaft in the direction of rotation. What is the new steady-state speed? Is this machine now a motor or a generator? (e) Suppose the machine is running uoloaded. What would the final steady-state speed of the rotor be if the flux density were reduced to $0.20 \mathrm{~T}$ ?

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