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An extension cord is used with an electric weed trimmer that has a resistance of 17.9 Ω. The extension cord is made of copper (resistivity 1.72 x 10-8 ohm m) wire that has a cross-sectional area of 1.71 x 10-6 m2. The combined length of the two wires in the extension cord is 86.3 m. (a) Determine the resistance of the extension cord. (b) The extension cord is plugged into a 120-V socket. What voltage is applied to the trimmer itself?

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Answer:

(a) [tex]R_{c}=0.87ohms[/tex]

(b) [tex]V_{T}=114.44V[/tex]

Explanation:

Part (a)

The total length of copper cord L=86.3 m

The cross sectional area A=1.71×10⁻⁶m²

The resistivity of copper p=1.72×10⁻⁸Ω

Thus the resistance of extension cord is

[tex]R_{c}=p\frac{L}{A}\\R_{c}=(1.72*10^{-8} )\frac{86.3}{1.71*10^{-6}}\\R_{c}=0.87ohms[/tex]

Part (b)

The resistance of trimmer Rt=17.9 ohms

When voltage of 120V is applied then the current I is passing through series circuit is

[tex]I=\frac{120V}{R_{c} +R_{T} }\\I=\frac{120V}{0.87 +17.9 } \\I=6.4A[/tex]

Thus the voltage across the trimmer is:

[tex]V_{T}=IR_{T}\\V_{T}=(6.4)*(17.9)\\V_{T}=114.44V[/tex]

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