A 100-W lightbulb has a resistance of about $12 \Omega$ when cold $(20^{\circ} \mathrm{C})$ and $140 \Omega$ when on (hot). Estimate the temperature of the filament when hot assuming an average temperature coefficient of resistivity $\alpha=0.0060\left(\mathrm{C}^{\circ}\right)^{-1}$.

t a point high in the Earth's atmosphere, $\mathrm{He}^{2+}$ ions in a concentration of $2.8 \times 10^{12} / \mathrm{m}^3$ are moving due north at a speed of $2.0 \times 10^6 \mathrm{~m} / \mathrm{s}$. Also, a $7.0 \times 10^{11} / \mathrm{m}^3$ concentration of $\mathrm{O}_2^{-}$ions is moving due south at a speed of $6.2 \times 10^6 \mathrm{~m} / \mathrm{s}$. Determine the magnitude and direction of the current density $\overrightarrow{\mathbf{j}}$ at this point.

The unit kilowatt-hour is a measure of $(a)$ the rate at which energy is transformed. $(b)$ power. $(c)$ an amount of energy. $(d)$ the amount of power used per second.

Battery-powered electricity is very expensive compared with that available from a wall receptacle. Estimate the cost per $\mathrm{kWh}$ of an alkaline AA-cell (cost $\$ 1.25$ ).

Battery-powered electricity is very expensive compared with that available from a wall receptacle. Estimate the cost per $\mathrm{kWh}$ of an alkaline D-cell $(\operatorname{cost} \$ 1.70)$

Battery-powered electricity is very expensive compared with that available from a wall receptacle. Estimate the cost per $\mathrm{kWh}$ of $(a)$ an alkaline D-cell $(\operatorname{cost} \$ 1.70)$. These batteries can provide a continuous current of $25 \mathrm{~mA}$ for $820 \mathrm{~h}$ and $120 \mathrm{~h}$, respectively, at $1.5 \mathrm{~V}$. Compare to normal 120 - $\mathrm{V}$ ac house current at $\$ 0.10 / \mathrm{kWh}$.

How much coal (which produces $7500 \mathrm{kcal} / \mathrm{kg}$ ) must be burned by a $35 \%$-efficient power plant to provide the yearly needs of a household which uses the following: A $2.2 \mathrm{~kW}$ heater $2.0 \mathrm{~h} / \mathrm{day}$ ("on" time), four $100 \mathrm{~W}$ lightbulbs $6.0 \mathrm{~h} / \mathrm{day}$, a $3.0 \mathrm{~kW}$ electric stove element for a total of $1.0 \mathrm{~h} / \mathrm{day}$, and miscellaneous power amounting to $2.0 \mathrm{kWh}$ /day.

A particular household uses a $2.2 \mathrm{~kW}$ heater $2.0 \mathrm{~h} /$ day ("on" time), four $100 \mathrm{~W}$ lightbulbs $6.0 \mathrm{~h} / \mathrm{day}$, a $3.0 \mathrm{~kW}$ electric stove element for a total of $1.0 \mathrm{~h} /$ day, and miscellaneous power amounting to $2.0 \mathrm{kWh}$ /day. If electricity costs $\$ 0.115$ per $\mathrm{kWh}$, what will be their monthly bill $(30 \mathrm{~d})$ ?

A particular household uses a $2.2~\mathrm{kW}$ heater $2.0 \mathrm{~h} /$day ("on" time), four $100~\mathrm{W}$ lightbulbs $6.0 \mathrm{~h} /$day a $3.0~\mathrm{kW}$ electric stove element for a total of $1.0 \mathrm{~h} /$ day, and miscellaneous power amounting to $2.0 \mathrm{kWh} /$ day. How much coal (which produces $7500 \mathrm{kcal} / \mathrm{kg}$ ) must be burned by a $35 \%$-efficient power plant to provide the yearly needs of this household?

A particular household uses a 1.8-kW heater 3.0 h/day ("on" time), four 100-W lightbulbs 6.0 h/day, a 3.0-kW electric stove element for a total of 1.4 h/day, and miscellaneous power amounting to 2.0 kWh/day. If electricity costs $0.105 per kWh, what will be their monthly bill (30 d)?

Estimate at what temperature copper will have the same resistivity as tungsten does at $20^{\circ} \mathrm{C}$.

Enzyme immunoassay tests are used to screen blood specimens for the presence of antibodies to HIV, the virus that causes AIDS. Antibodies indicate the presence of the virus. The test is quite accurate but is not always correct. Here are approximate probabilities of positive and negative test results when the blood tested does and does not actually contain antibodies to HIV:

Suppose that 1 % of a large population carries antibodies to HIV in its blood.

(a) Draw a tree diagram for selecting a person from this population (outcomes: antibodies present or absent) and for testing his or her blood (outcomes: test positive or negative).

(b) What is the probability that the test is positive for a randomly chosen person from this population?

Suppose that for the general population, 1 in 5000 people carries the human immunodeficiency virus (HIV). A test for the presence of HIV yields either a positive (+) or negative (-) response. Suppose the test gives the correct answer 99% of the time. What is P[-|H], the conditional probability that a person tests negative given that the person does have the HIV virus? What is P[H|+], the conditional probability that a randomly chosen person has the HIV virus given that the person tests positive?

Enzyme immunoassay (EIA) tests are used to screen blood specimens for the presence of antibodies to HIV, the virus that causes AIDS. Antibodies indicate the presence of the virus. The test is quite accurate but is not always correct. Here are approximate probabilities of positive and negative EIA outcomes when the blood tested does and does not actually contain antibodies to HIV:

$$\begin{array}{lcc} & \text { Test } & \text { Result } \\ \hline & + & - \\ \hline \text { Antibodies present } & 0.9985 & 0.0015 \\ \text { Antibodies absent } & 0.006 & 0.994 \\ \hline \end{array}$$

Suppose that 1% of a large population carries antibodies to HIV in their blood. What is the probability that the EIA test is positive for a randomly chosen person from this population?