An electric heater is constructed by applying a potential difference of 120 V ac

Question

An electric heater is constructed by applying a potential difference of 120 V across a Nichrome wire that has a total resistance of 7.80 Ohm. Find the current carried by the wire and the power rating of the heater. Conceptualize Nichrome wire has high resistivity and is often used for heating elements in toasters, irons, and electric heaters. Therefore, we expect the power delivered to the wire to be relatively high. Categorize We evaluate the power, so we categorize this example as a substitution problem. Find the current in the wire: Find the power rating using the expression P= I2R: What if we have another heater rated at 120 V with power 3.2 kW? What is the resistance of the heater, and the current when it is under normal operation? If we connect it a 240 V source, assuming that it still works, what will be the actual power consumption now?

Explanation / Answer

(A) V = 120 V

Power = P = 3.2 Kw = 3200 W

P = V^2 / R

3200 = 120^2 / R

R = 120 * 120 / 3200

R = 4.5 ohm

I = V / R

= 120 / 4.5

I = 26.67 A

(b) New V = 240 V

R = 4.5 ohm

New power = V^2 / R

= 240 * 240 / 4.5

= 12800 W

new power = 12.8 KW

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