Students were asked to answer a question at school and to claim what is most important for them to succeed. From the numerous replies, one which that stood out was practice. Successful persons aren’t born successful; they become successful through hard work and dedication. This is how you can get your goals. followed below are one of the answer and question example that you can certainly benefit from to practice and elevate your knowledge and also give you insights that would guide you to sustain your study in school.
Question:
An aluminum wire of length 1.0 meter has a resistance of 9.0×10^-3 ohm. If the wire were cut into two equal lengths, each length would have a resistance of
Answer:
Each length of wire would have a resistance of 4.5 × 10⁻³ Ω.
Since resistance R = ρl/A where
- ρ = conductivity of aluminum,
- l = length and
- A = cross-sectional area.
Since ρ and A are constant for the aluminum wire, R ∝ l
So. R₂/R₁ = l₂/l₁ where
- R₁ = initial resistance of wire,
- R₂ = resistance after wire is cut in two,
- l₁ = initial length of wire = 1 m and,
- l₂ = final length of wire = l₁/2
Now, since the length of the wire is cut into two, l₂ = l₁/2
So, R₂/R₁ = l₁/2 ÷ l₁
R₂/R₁ = 1/2
R₂ = R₁/2
R₂ = 9.0 × 10⁻³ Ω/2
R₂ = 4.5 × 10⁻³ Ω
So, each length of wire would have a resistance of 4.5 × 10⁻³ Ω.
Learn more about resistance here:
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