20.4 Electric Power and Energy

What will be the ratio of the resistance of a 120 W, 220 V lamp to that of a 100 W, 110 V lamp?

What is the power of a $1.00 \times \text{10}^{\text{2}} \text{MV}$ lightning bolt having a current of $2.00 × 10^{\text{4}} \text{A}$?

Find the power dissipated in each of these extension cords: (a) an extension cord having a $0 . \text{0600} - \Omega$ resistance and through which 5.00 A is flowing; (b) a cheaper cord utilizing thinner wire and with a resistance of $0 . \text{300} \Omega .$

Show that the units $1 \text{ V}^{2} / \Omega = 1 \text{ W}$, as implied by the equation $P = V^{2} / R$.

Verify the energy unit equivalence that $1 \text{ kW} \cdot \text{h }=\text{ 3} . \text{60} \times \text{10}^{6} \text{ J}$.

What would be the maximum cost of a CFL such that the total cost (investment plus operating) would be the same for both CFL and incandescent 60-W bulbs? Assume the cost of the incandescent bulb is 25 cents and that electricity costs $\text{10 cents}/\text{kWh}$. Calculate the cost for 1000 hours, as in the cost effectiveness of CFL example.

Alkaline batteries have the advantage of putting out constant voltage until very nearly the end of their life. How long will an alkaline battery rated at $1 . \text{00 A} \cdot \text{h}$ and 1.58 V keep a 1.00-W flashlight bulb burning?

The average television is said to be on 6 hours per day. Estimate the yearly cost of electricity to operate 100 million TVs, assuming their power consumption averages 150 W and the cost of electricity averages $\text{12} . 0 \text{ cents}/\text{kW} \cdot \text{h}$.

00-gauge copper wire has a diameter of 9.266 mm. Calculate the power loss in a kilometer of such wire when it carries $1.00 \times \text{10}^{\text{2}} \text{A}$.

(a) What energy is dissipated by a lightning bolt having a 20,000-A current, a voltage of $1.00 \times \text{10}^{\text{2}} \text{MV}$, and a length of 1.00 ms? (b) What mass of tree sap could be raised from $\text{18} . 0º \text{C}$ to its boiling point and then evaporated by this energy, assuming sap has the same thermal characteristics as water?

How much time is needed for a surgical cauterizer to raise the temperature of 1.00 g of tissue from $\text{37} . 0º \text{C}$ to $\text{100}º \text{C}$ and then boil away 0.500 g of water, if it puts out 2.00 mA at 15.0 kV? Ignore heat transfer to the surroundings.

(a) An aluminum power transmission line has a resistance of $0 . \text{0580} \Omega / \text{km}$. What is its mass per kilometer? (b) What is the mass per kilometer of a copper line having the same resistance? A lower resistance would shorten the heating time. Discuss the practical limits to speeding the heating by lowering the resistance.

(a) What current is needed to transmit $1.00 \times \text{10}^{\text{2}} \text{MW}$ of power at 480 V? (b) What power is dissipated by the transmission lines if they have a $1 . \text{00} - \Omega$ resistance? (c) What is unreasonable about this result? (d) Which assumptions are unreasonable, or which premises are inconsistent?