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# What is the resistance of a lightbulb that uses an average power of 75.0 W when connected to a 60.0-Hz power source having a maximum voltage of 170 V?

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The frequency of the source is given to be $f = 60$ Hz.

The angular frequency thus becomes

\begin{align*} &\omega=2\pi\times\text{frequency} \tag{---formula1}\\ \\ &\omega=2\pi\times 60\\ \\ &\omega=120\pi \tag{---1}\\ \end{align*}

The maximum voltage of the source is given to be $V_{max} = 170 \text{ V}$

R.M.S Voltage of the source in terms of maximum Voltage is given by

\begin{align*} V_{rms} &= \dfrac{V_{max}}{\sqrt{2}}\\ \\ V_{rms} &= \dfrac{170}{\sqrt{2}}\\ \\ V_{rms} &= 120.208 \text{ V} \tag{---2}\\ \end{align*}

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