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The problem you're working on is related to calculating the total energy \( U \) expended by a 100W light bulb, using the power \( P(t) \) over time. The resistance of the light bulb is \( R = 144 \, \Omega \), and the voltage is given by an oscillating function of time: 

\[
V(t) = V_0 \sin(2 \pi f t),
\]
where:
- \( V_0 = 110 \, \text{V} \) (the maximum voltage),
- \( f = 60 \, \text{Hz} \) (the frequency of the alternating current).

The expression for the energy expended over a time period \( T \) is the integral of the power over that time:

\[
U = \int_0^T P(t) \, dt.
\]

Now, power \( P(t) \) is related to the instantaneous voltage \( V(t) \) and the resistance \( R \) of the light bulb through the relation:

\[
P(t) = \frac{V(t)^2}{R}.
\]

Substituting the voltage expression into this equation, we get:

\[
P(t) = \frac{(V_0 \sin(2\pi f t))^2}{R} = \frac{V_0^2 \sin^2(2\pi f t)}{R}.
\]

Thus, the total energy \( U \) is:

\[
U = \int_0^T \frac{V_0^2 \sin^2(2\pi f t)}{R} \, dt.
\]

Would you like me to solve this integral to determine the total energy expended by the bulb over a given period \( T \)? 

If so, please specify the time \( T \), or I can proceed with assuming a standard period like one second.

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**Related questions:**
1. How is power calculated from voltage and resistance?
2. What are the steps to solve the integral of a trigonometric function squared?
3. How does the frequency \( f \) of an alternating current affect the energy calculation?
4. How do you calculate the root-mean-square (RMS) value of an AC voltage?
5. What is the role of resistance in energy dissipation in electrical circuits?

**Tip:** When working with AC circuits, it's helpful to remember that the root-mean-square (RMS) voltage is used to compute average power instead of peak voltage.

A 100W light bulb has resistance R = 144Ω (ohms) when attached to household current, where the voltage varies as V = V₀sin(2πft), where V₀ = 110V and f = 60Hz. The energy (in joules) expended by the bulb over a period of T seconds is U = ∫₀ᵀ P(t) dt.

This problem explores the energy expended by a 100W light bulb over time using AC voltage, trigonometric functions, and calculus. Key concepts include Ohm's Law, power dissipation, and the integration of sinusoidal functions. Suitable for undergraduate-level students in physics or electrical engineering.

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