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A single 9-V alkaline battery can deliver a charge of 565 mA h. Two of these batteries are connected one after the other to power a 32 ohm heating resistor at 18 V, drawing 0.56 A. About how long will this heater run before the batteries are exhausted?

A2.0 hours
B1.0 hour
C20 hours
D0.56 hours
Answer & Solution
Correct answer: A. 2.0 hours
1. Two batteries connected one after the other are stated to deliver a combined charge of 565 mA h + 565 mA h = 1130 mA h, or 1.130 A h. 2. The heater draws a steady current of I = 0.56 A. 3. Runtime is the total available charge divided by the current drawn: t = charge / I. 4. Substitute with consistent units: t = 1.130 A h / 0.56 A. 5. t is approximately 2.0 hours. 6. 1.0 hour would result from using only one battery's charge instead of the combined charge of both. 7. 20 hours would result from a tenfold arithmetic slip in the current or charge value. _Source: OpenStax Physics (CC BY 4.0), Ch 19 "Electrical Circuits", section Boot Warmers_
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