A nichrome heater element has a resistance of 2 £2/m. To build a 1 kW heater operating at 200 V, the required wire length is_____________?
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Answer: D. 20 m
Explanation
Using the power formula requires calculating the total required resistance to be forty ohms. Dividing the total resistance by the resistance per meter yields the required wire length. Forty ohms divided by two ohms per meter results in a wire length of twenty meters. Electrical power is calculated as voltage squared divided by the circuit resistance value. Resistance per unit length specifies how many ohms each meter of heater wire contributes. Total resistance equals the product of resistance per meter and the total wire length.
Heater element design requires precise calculations to ensure correct thermal power generation. Using wrong wire lengths would cause overheating or insufficient heating in appliances. Nichrome wire is standard for heating elements due to its high resistance and heat tolerance. Option A is incorrect and represents an overestimation of the required wire length. Option B is wrong because it results from incorrect arithmetic during power calculations. Option C is incorrect because it would double the intended resistance and halve the power.
- Subject
- Engineering
- Category
- Electrical Engineering
- Topic
- —
- Difficulty
- medium
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