In Example 22.6 the length of a \(60 \mathrm{~W}, 240 \Omega\) lightbulb filament was calculated to be \(60 \mathrm{~cm}\).

a. If the potential difference across the filament is \(120 \mathrm{~V}\), what is the strength of the electric field inside the filament?

b. Suppose the length of the bulb's filament were doubled without changing its diameter or the potential difference across it. What would the electric field strength be in this case?

c. Remembering that the current in the filament is proportional to the electric field, what is the current in the filament following the doubling of its length?

d. What is the resistance of the filament following the doubling of its length?

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EXAMPLE 22.6 The length of a lightbulb filament We calculated in Example 22.5 that a 60 W lightbulb has a resistance of 240 2. At the operating temperature of the tungsten filament, the resistivity is approximately 5.0 10 m. If the wire used to make the filament is 0.040 mm in diameter (a typical value), how long must the filament be? PREPARE The resistance of a wire depends on its length, its cross-section area, and the material of which it is made.