A $40-$turn rectangular coil with dimensions $0\mathrm{.}13$ m $0\mathrm{.}45$ m rotates in a uniform magnetic field of magnitude $0\mathrm{.}65$ T at $3,900$ rev$/$min$.($Use the following as necessary: t$.$ Do not use other variables, substitute numerical values. Assume t is in seconds.$)$

$($a$)$

Determine the emf induced in the coil as a function of time. $($Assume the plane of the coil is perpendicular to the magnetic field at

t $=0.$

Further, assume is in volts.$)$

$($t$)=$

$($b$)$

If the coil is connected to a $1,000$ resistor, what is the power as a function of time required to keep the coil turning at $3,900$ rpm$?($Assume P is in watts.$)$

P$($t$)=$

$($c$)$

Answer part $($b$)$ if the coil is connected to a $2,000$ resistor.

P$($t$)=$

$$

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