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Resistors

Resistors dissipate energy in electric circuits, but their behavior is found time and again in diverse phenomena from the flux of biomass in bacterial cells to the flow of cars on city traffic grids.

Energy Dissipation by a Resistor

If a current of \(4.00\text{ A}\) flows in a copper wire with a cross-sectional area of \(2.70 \times 10^{-6}\text{ m}^2\) and a length of \(5.40\text{ m},\) approximately how much electrical energy is transferred to thermal energy in \(15\text{ min}?\)

The resistivity of copper is \(1.69 \times 10^{-8}\,\Omega\cdot\text{m}.\)

Suppose that energy is dissipated at the rate of \(P_1 = 0.600\text{ W}\) in a resistor which is connected between the terminals of a \(V_1 = 4.20\text{ V}\) battery. If the same resistor is connected between the terminals of a \(V_2 = 2.10\text{ V}\) battery, at what rate is energy dissipated?

James dries his hair with a hair dryer every morning. The dryer uses \( 64 \text{ W} \) of power and the current supplied is \( 0.4 \text{ A}. \) What is the resistance of the dryer?

A Nichrome wire that has a cross sectional area of \(2.50 \times 10^{-6}\text{ m}^2\) is connected to a potential difference of \(75.0\text{ V}.\) If the wire dissipates \(4000\text{ W},\) what is its approximate length?

Nichrome has a resistivity of \(6.00 \times 10^{-7}\,\Omega\cdot\text{m}.\)

Consider a certain length of uniform heating wire which has a resistance of \(R=72\,\Omega.\) At what rate is energy dissipated when (a) a potential difference of \(360\text{ V}\) is applied across the full length of the wire, and (b) the wire is cut in half and the same potential difference as in (a) is applied across the length of each half?

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