Subjects physics

Charge Smoke Detector 9A1F60

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1. **State the problem:** Calculate how much charge passes through a smoke detector connected to a 9.0 V cell transferring energy at a rate of $1.0 \times 10^{-4}$ W in one day. 2. **Formula and explanation:** Power $P$ is the rate of energy transfer, and it relates to voltage $V$ and current $I$ by the formula: $$P = VI$$ Charge $Q$ passing through in time $t$ is related to current by: $$Q = It$$ 3. **Calculate current $I$:** $$I = \frac{P}{V} = \frac{1.0 \times 10^{-4}}{9.0} = 1.11 \times 10^{-5} \text{ A}$$ 4. **Calculate time $t$ in seconds:** One day has 24 hours, each hour 3600 seconds: $$t = 24 \times 3600 = 86400 \text{ s}$$ 5. **Calculate charge $Q$:** $$Q = It = (1.11 \times 10^{-5}) \times 86400 = 0.96 \text{ C}$$ 6. **Simplify and match answer:** $0.96 \approx 0.98$ C, so the closest answer is B. **Final answer:** B 0.98 C