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You want 10 W of heat output from a resistor heater powered by two 9-V batteries connected one after the other. What total resistance should the heater have?
A8.1 ohm
B1.8 ohm
C324 ohm
D32 ohm
Answer & Solution
Correct answer: D. 32 ohm
1. Two 9-V batteries connected one after the other give a combined voltage of V = 9 V + 9 V = 18 V.
2. Use the power expression that involves voltage and resistance: P = V^2 / R.
3. Rearrange for resistance: R = V^2 / P.
4. Substitute with SI units: R = (18 V)^2 / (10 W) = 324 / 10 ohm = 32.4 ohm, rounding to 32 ohm.
5. 8.1 ohm would result from using a single 9 V battery instead of the combined 18 V.
6. 324 ohm forgets to divide by the power at all, leaving only the numerator of the calculation.
_Source: OpenStax Physics (CC BY 4.0), Ch 19 "Electrical Circuits", section Boot Warmers_
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