A $50-$turn rectangular coil with dimensions rotates in a uniform magnetic f ield of magnitude $0\mathrm{.}75$ T at $3600$ rev$/$min$.($a$)$ Determine the emf induced in the coil as a function of time. $($b$)$ If the coil is connected to a resistor, what is the power as a function of time required to keep the coil turning at $3600$ rpm$?($c$)$ Answer part $($b$)$ if the coil is connected to a $2000-$resistor.