You plug a 9-Volt battery into a smoke detector. Attached to the circuit within

Question

You plug a 9-Volt battery into a smoke detector. Attached to the circuit within the smoke detector is an energy meter, showing you how much energy has been released by the electrons traveling through the circuit since the battery was last replaced. If the battery dies after 1.0 Mega joule of energy has been transferred, what is the total amount of charge that has passed through the circuit? How many electrons is this? Follow-up: if the circuit was continuously operating at 50 mA of current (a reasonable current for small electronic devices), how long was the battery in the smoke detector until it died? Express your answer in the most reasonable units. Do you think the average battery rated for a smoke detector would typically be more powerful than this one, about the same, or less powerful?

Explanation / Answer

electric potential energy is given by:

U = q V

q = U/V

q = 1 x 10^6/9 = 1.11 x 10^5 C

One electron has e = 1.6 x 10^-19 C

So the number of electrosnw ouwld be

N = q/e = 1.11 x 10^5/(1.6 x 10^-19) = 6.94 x 10^23 electrons

Hence, N = 6.94 x 10^23 electrons

I = 50 mA = 50 x 10^-3 A

P = E/t = V I

t = E/V I = 1 x 10^6/9 x 50 x 10^-3 = 2.22 x 10^6 s

Hence, t = 2.22 x 10^6 s

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