Answer:
(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
<u>R = 224.37 Ω</u>
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(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)
<u>ρ = 7.18 x 10⁻⁷ Ω.m</u>