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# A simple generator has a square armature $6.0 \mathrm{~cm}$ on a side. The armature has $85$ turns of $0.65 \mathrm{~cm}$ diameter copper wire and rotates in a $0.65 \mathrm{~T}$ magnetic field. The generator is used to power a lightbulb rated at $12.0 \mathrm{~V}$ and $25.0 \mathrm{~W}$. At what rate should the generator rotate to provide $12.0 \mathrm{~V}$ to the bulb? Consider the resistance of the wire on the armature.

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$\color{#4257b2}\text{Givens:}$

We are given a generator of a square armature rotating in a magnetic field to power a light bulb,

• $l= 6\;\mathrm{cm}$: is the length of the square armature of the generator.

• $N= 85\;\mathrm{turns}$: is the number of loops of the generator coil.

• $d_w= 0.65\;\mathrm{mm}$: is the diameter of the copper wire of the generator coil.

• $B= 0.65\;\mathrm{T}$: is the magnetic field in which the generator rotates.

• $V= 12\;\mathrm{V}$: is the voltage needed to turn on the light bulb.

• $P= 25\;\mathrm{W}$: is the power rated for the light bulb.

We are required to evaluate the angular frequency $\omega$ by which the generator should rotate to turn on the light bulb.

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