Problem $6$: A permenant magnet DC generator has a $\backslash ($ k $\backslash$phi $\backslash )$ value of $2\mathrm{.}5$ Wb and an $\backslash (\backslash$mathrm$\{$R$\}\_\{\backslash$mathrm$\{$A$\}\}\backslash )$ of $\backslash (1\mathrm{.}5\backslash$Omega $\backslash )$ with negligible rotational losses. The prime mover rotates the armature at a speed of $1000$ rpm $.$ Determine the no$-$load voltage, the full$-$load voltage, and the torque required by the prime mover at full load if the fullload current required by the load is $18$ A $.(10$ points$)$

Problem $7$: A permenant magnet DC generator has a $\backslash ($ k $\backslash$phi $\backslash )$ value of $1\mathrm{.}5$ Wb and an $\backslash (\backslash$mathrm$\{$R$\}\_\{\backslash$mathrm$\{$A$\}\}\backslash )$ of $\backslash (3\backslash$Omega $\backslash ).$ The prime mover rotates the armature at a speed of $1200$ rpm $.$ Determine the no$-$load voltage, the full$-$load voltage, and the power required by the prime mover at full load if the full$-$load power required by the load is $120$ W $($assumming most of the power is delivered to the load$)$ neglecting rotational losses. Note: Need accuracy better than $3$ significant figures. $(15$ points$)$

Problem $8$: A stepper motor with $5$ phases and $6$ poles has the speed$-$torque curve shown.

a$)$ What is the step size for the stepper motor in degrees? $(5$ points$)$

b$)$ What is the speed of the stepper motor in rpm if the motor is driven by pulses sent at $60,000$ pulses per minute if the develop torque from the stepper motor is $1\mathrm{.}2$ Nm $?(5$ points$)$

c$)$ What would be the motor speed in rpm if the motor is driven by pulses sent at $30,000$ pulses per minute if the develop torque from the stepper motor is $1\mathrm{.}8$ Nm $?(5$ points$)$