A motorcyclist is making an electric vest that, when connected to the motorcycle's 12 V battery, will warm her on cold rides. She is using 0.25-mm-diameter copper wire, and she wants a current of 5.5A in the wire. What length wire must she use?
The resistance can be calculated by the formula,
$$ R=\frac{\rho l}{A} $$
Here, \(l\) is the length of the wire, \(\rho\) is the resistivity and \(A\) is the area.
The area of the copper wire will be,
$$ \begin{aligned} A &=\pi r^{2} \\ &=\pi\left(\left(\frac{0.25 \mathrm{~mm}}{2}\right)\left(\frac{10^{-3} \mathrm{~m}}{1 \mathrm{~mm}}\right)\right)^{2} \\ &=4.91 \times 10^{-8} \mathrm{~m}^{2} \end{aligned} $$
The resistivity of copper wire is, \(\rho=1.68 \times 10^{-8} \Omega \cdot \mathrm{m}\) Also, with the help of Ohm's law, \(R=\frac{V}{I}\)
Substitute \(\frac{V}{I}\) for \(R\) in equation (1).
$$ \begin{aligned} \frac{V}{I} &=\frac{\rho l}{A} \\ l &=\frac{V A}{I \rho} \\ &=\frac{(12 \mathrm{~V})\left(4.91 \times 10^{-8} \mathrm{~m}^{2}\right)}{(5.5 \mathrm{~A})\left(1.68 \times 10^{-8} \Omega \cdot \mathrm{m}\right)} \\ &=6.4 \mathrm{~m} \end{aligned} $$
A motorcyclist is making an electric vest that, when connected to the motorcycle's 12 V battery,...
A motorcyclist is making an electric vest that, when connected to the motorcycle's 12 V battery, will warm her on cold rides. She is using 0.23-mm-diameter copper wire, and she wants a current of 5.1 A in the wire.What length wire must she use?
A motorcyclist is making an electric vest that, when connected to the motorcycle's 12 V battery, will warm her on cold rides. She is using 0.21-mm-diameter copper wire, and she wants a current of 4.4 A in the wire. What length wire must she use?
A motorcyclist is making an electric vest that, when connected to the motorcycle's 12 V battery, will warm her on cold rides. She is using 0.22-mm-diameter copper wire, and she wants a current of 4.3 A in the wire. What length wire must she use?
A motorcyclist is making an electric vest that, when connected to the motorcycle's 12 V battery, will warm her on cold rides. She is using 0.22-mm-diameter copper wire, and she wants a current of 5.5 A in the wire. What length wire must she use? L= __(value)____ ___(unit)____
1) A capacitor is charged to 8.0×10−4 C , then discharged by connecting a wire between the two plates. 20 μs after the discharge begins, the capacitor still holds 15% of its original charge. What was the average current during the first 20 μsof the discharge? 2) What is the resistance of a 1.0-m-long copper wire that is 0.40 mm in diameter? b) What is the resistance of a 20-cm-long piece of iron with a 1.5 mm × 1.5 mm...
What voltage will produce 0.35 A of current through a 4800-Ω resistor? A 9.0-V battery is connected to a bulb whose resistance is 2.2 Ω How many electrons leave the battery per minute? What is the resistance of a 7.4-m length of copper wire 1.4 mm in diameter? The resistivity of copper is 1.68×10−8Ω⋅m A 12-V battery causes a current of 0.72 A through a resistor. What is its resistance? How many joules of energy does the battery lose in...
A 2.0m length of metal wire is connected to a 1.5 V battery, and a current of 5.0mA flows through it. What is the diameter of the wire? (The resistivity of metal is 2.24
You want to design a portable electric blanket that runs on a 1.5 V battery. If you use copper wire with a 0.50 mm diameter as the heating element, how long should the wire be if you want to generate 15 W of heating power?
The terminals of a 0.700 V watch battery are connected by a 120 - m - long gold wire with a diameter of 0.200 mm. Part A What is the current in the wire? Express your answer using three significant figures. I = mA
The terminals of a 0.70 V watch battery are connected by a 140-m-long gold wire with a diameter of 0.200 mm . What is the current in the wire? answer should be in mA