9.5 Electrical energy and power  (Page 7/8)

Your electric bill gives your consumption in units of kilowatt-hour (kW $·$ h). Does this unit represent the amount of charge, current, voltage, power, or energy you buy?

Resistors are commonly rated at $\frac{1}{8}\text{W}$ , $\frac{1}{4}\text{W}$ , $\frac{1}{2}\text{W}$ , 1 W and 2 W for use in electrical circuits. If a current of $I=2.00\text{A}$ is accidentally passed through a $R=1.00\text{Ω}$ resistor rated at 1 W, what would be the most probable outcome? Is there anything that can be done to prevent such an accident?

An immersion heater is a small appliance used to heat a cup of water for tea by passing current through a resistor. If the voltage applied to the appliance is doubled, will the time required to heat the water change? By how much? Is this a good idea?

A $20.00\text{-V}$ battery is used to supply current to a $10\text{-k}\text{Ω}$ resistor. Assume the voltage drop across any wires used for connections is negligible. (a) What is the current through the resistor? (b) What is the power dissipated by the resistor? (c) What is the power input from the battery, assuming all the electrical power is dissipated by the resistor? (d) What happens to the energy dissipated by the resistor?

What is the maximum voltage that can be applied to a $10\text{-k}\text{Ω}$ resistor rated at $\frac{1}{4}\text{W}$ ?

A heater is being designed that uses a coil of 14-gauge nichrome wire to generate 300 W using a voltage of $V=110\text{V}$ . How long should the engineer make the wire?

An alternative to CFL bulbs and incandescent bulbs are light-emitting diode (LED) bulbs. A 100-W incandescent bulb can be replaced by a 16-W LED bulb. Both produce 1600 lumens of light. Assuming the cost of electricity is $0.10 per kilowatt-hour, how much does it cost to run the bulb for one year if it runs for four hours a day?

The power dissipated by a resistor with a resistance of $R=100\text{Ω}$ is $P=2.0\text{W}$ . What are the current through and the voltage drop across the resistor?

Running late to catch a plane, a driver accidentally leaves the headlights on after parking the car in the airport parking lot. During takeoff, the driver realizes the mistake. Having just replaced the battery, the driver knows that the battery is a 12-V automobile battery, rated at 100 $\text{A}·\text{h}$ . The driver, knowing there is nothing that can be done, estimates how long the lights will shine, assuming there are two 12-V headlights, each rated at 40 W. What did the driver conclude?

A physics student has a single-occupancy dorm room. The student has a small refrigerator that runs with a current of 3.00 A and a voltage of 110 V, a lamp that contains a 100-W bulb, an overhead light with a 60-W bulb, and various other small devices adding up to 3.00 W. (a) Assuming the power plant that supplies 110 V electricity to the dorm is 10 km away and the two aluminum transmission cables use 0-gauge wire with a diameter of 8.252 mm, estimate the percentage of the total power supplied by the power company that is lost in the transmission. (b) What would be the result is the power company delivered the electric power at 110 kV?

A 0.50-W, $220\text{-}\text{Ω}$ resistor carries the maximum current possible without damaging the resistor. If the current were reduced to half the value, what would be the power consumed?