1. What is the effect on the current in a wire if both the voltage across it and its resistance are doubled? If both are halved?
2. The wattage marked on a lightbulb is not an inherent property of the bulb, but depends on the voltage to which it is connected, usually 110 or 120 V. How many amperes flow through a 60-W bulb connected in a 120-V circuit?
3. Rearrange the equation current = voltage/resistance to express resistance in terms of current and voltage. Then solve the following: A certain device in a 120-V circuit has a current rating of 20 A. What is the resistance of the device (how many ohms)?
4. Using the formula power = current X voltage, find the current drawn by a 1200-W toaster connected to 120 V. Then, using the method from the previous problem, show that the resistance of the roaster is 12Ω.
5. The total charge that an automobile battery can supply without being recharged is given in terms of ampere-hours. A typical 12-V battery has a rating of 60 ampere-hours (60 A for 1 h, 30 A for 2 h, and so on). Suppose that you forget to turn the headlights off in your parked automobile. If each of the two headlights draws 3 A, how long will it be before your battery is "dead"?
6. Show that operating a 100-W lamp continuously for 1 week when the power utility rate is 15C/kWh costs $2.52.
7. A 4-W night-light is plugged into a 120-V circuit and operates continuously for 1 year. Find the following: (a) the current it draws, (b) the resistance of its filament, (c) the energy consumed in a year. (d) Then show that for a utility rate of 15c/kWh the cost for a year's operation is $5.25.
8. An electric iron connected to a 110-V source draws 9 A of current. Show that the amount of heat it generates in a minute is nearly 60,000 J.
9. Show in the previous problem that 540 C of charge flow through the iron in 1 minute.
10. In periods of peak demand, power companies lower their voltage. This saves them power (and saves you money!). To see the effect, consider a 1200-W coffeemaker that draws 10 A when connected to 120 V. Suppose the voltage is lowered by 10% to 108 V. By how much does the current decrease? By how much does the power decrease? (Caution: The 1200-W label is valid only when 120 V is applied. When the voltage is lowered, it is the resistance of the toaster, not its power that remains constant.)