A voltmeter connected across the terminals of a tungsten-filament light bulb measures 116 V when an ammeter in line with the bulb registers a current of 0.517 A. HINT (a) Find the resistance of the light bulb. (Enter your answer in ohms.) Ω (b) Find the resistivity of tungsten (in Ω · m) at the bulb's operating temperature if the filament has an uncoiled length of 0.553 m and a radius of 2.33 ✕ 10−5 m. Ω · m

(a) R = 224.37 Ω

(b) ρ = 7.18 x 10⁻⁷ Ω.m

Explanation:

(a)

From Ohm's Law we have the following formula:

V = IR

where,

V = Voltage = 116 volts

I = Current Passing through bulb = 0.517 A

R = Resistance of light bulb = ?

Therefore,

116 volts = (0.517 A)R

R = 116 volts/0.517 A

R = 224.37 Ω

(b)

Now, the formula of resistance of a wire is:

R = ρL/A

where,

ρ = resistivity of bulb = ?

R = Resistance = 224.37 Ω

L = Length of Wire = 0.533 m

A = Cross Sectional Area of Wire = πr² = π(2.33 x 10⁻⁵ m)² = 1.7 x 10⁻⁹ m²

Therefore,

224.37 Ω = ρ(0.533 m)/(1.7 x 10⁻⁹ m²)

ρ = (224.37 Ω)(1.7 x 10⁻⁹ m²)/(0.533 m)

ρ = 7.18 x 10⁻⁷ Ω.m

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