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Currents 11/19/08

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**Aluminum wiring has sometimes been used instead of copper for economy**

Aluminum wiring has sometimes been used instead of copper for economy. According to the National Electrical Code, the maximum allowable current for 12-gauge Cu wire with rubber insulation is 20 A. What should be the maximum allowable current in a 12-gauge Al wire if the power per unit length in the Al wire is the same as that in the Cu wire?

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**Problems A current of 4.82 A exists in a 12.4 resistor for 4.6 min.**

How much charge passes through any cross section of the resistor in this time? How many electrons does this correspond to?

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Problems A 5.12 A current is set up in an external circuit by a 6 V storage battery for 5.75 min. How much is the energy of the battery reduced?

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Problems A 12 V car battery carries an initial charge of 125 Ahr. Assuming that the potential across the terminals stay constant until the battery is completely discharged, how long can it deliver energy at 110 W?

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**Radial Resistance of a Coaxial Cable**

Figure 27.8 (Example 27.4) A coaxial cable. (a) Silicon fills the gap between the two conductors. a = cm b = 1.75 cm L = 15.0 cm = 640 m

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An experiment is conducted to measure the electrical resistivity of Nichrome in the form of wires with different lengths and cross-sectional areas. For one set of measurements, a student uses 30-gauge wire, which has a cross-sectional area of 7.30 × 10–8 m2. The student measures the potential difference across the wire and the current in the wire. For each of the measurements given in the table taken on wires of three different lengths, calculate the resistance of the wires and the corresponding values of the resistivity. What is the average value of the resistivity, and how does this value compare with the tabulated value? L (m) ΔV (V) I (A) R (Ω) ρ(Ω · m)

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**An electric car is designed to run off a bank of 12.0-V batteries with **

total energy storage of 2.00 × 107 J. If the electric motor draws 8.00 kW, what is the current delivered to the motor? If the electric motor draws 8.00 kW as the car moves at a steady speed of 20.0 m/s, how far will the car travel before it is “out of juice”? .

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A parallel-plate capacitor consists of square plates of edge length ℓ that are separated by a distance d, where d << ℓ. A potential difference ΔV is maintained between the plates. A material of dielectric constant κ fills half of the space between the plates. The dielectric slab is now withdrawn from the capacitor, as shown in the figure. a) Find the capacitance when the left edge of the dielectric is at a distance x from the center of the capacitor. b) If the dielectric is removed at a constant speed v, what is the current in the circuit as the dielectric is being withdrawn?

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