13.
The relationship between power, voltage, and resistance can be expressed as ...
P = V²/R
Solving for resistance, you find ...
R = V²/P
Filling in the given values, you get ...
R = (120 V)²/(360 W) = 40.0 Ω
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14.
⇒ The maximum power the device can dissipate without overheating.
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In practice, the power rating is chosen to meet several requirements, including legal, liability, reliability, life expectancy, and others. For components, there tend to be tradeoffs between power dissipation and reliability. (Higher reliability parts are given a lower power rating even though the process by which they are made is unchanged.) For appliances, there may be legal requirements involving wiring and insurance and fire protection.
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15.
The voltage divider formula is ...
V₁ = V₀×(R₂/(R₁+R₂))
where R₁ is the series resistor and R₂ is the resistor across which the voltage is being measured. V₀ is the voltage applied across the two resistances.
Filling in your numbers, you get
V₁ = 25 V × (7.5/(5+7.5)) = 15 V