Answer
$f=16.5Hz$
Work Step by Step
$A_a=3.6\times10^{-3}m^2$
$A_w=\pi r^2=\pi(\frac{0.59\times10^{-3}}{2})=2.734\times10^{-7}m^2$
$l_w=4sN=4\times0.06\times85=20.4m$
$R_w=\frac{1.68\times10^{-8}\times20.4}{2.734\times10^{-7}}=1.254\Omega$
$I_{rms}=\frac{P}{V}=\frac{25.0W}{12.0V}=2.08A$
$V_c=V_{lightbulb}+V_{armature}=12V+(2.083A\times1.254\Omega)=14.61V$
$V_{rms}=\frac{E}{\sqrt{2}}=\frac{NBA_{armature}(2\pi f)}{\sqrt{2}}$
$f=16.5Hz$
