27. Resistors & DC Circuits

A hair dryer operates at 120 V (the voltage produced by a household outlet), and outputs 1200 W of energy. For this problem, treat the hair dryer as a single resistor. 

(a) At what current does the hair dryer operate?
(b) What is the resistance of the hair dryer?

An incandescent lightbulb produces 100 W of light. If this lightbulb operates at 25% efficiency (meaning that out of all the power it generates, only 25% is released as light), what resistance must the lightbulb have if it operates at 120 V?

(II) A 12-V battery causes a current of 0.50 A through a resistor.

(b) how many joules of energy does the battery lose in a minute?

(I) The heating element of an electric oven is designed to produce 3.1 kW of heat when connected to a 240-V source. What must be the resistance of the element?

(I) An electric car uses a 45-kW (160-hp) motor. If the battery pack is designed for 340 V, what current would the motor need to draw from the battery? Neglect any energy losses in getting energy from the battery to the motor.

(II) A 120-V hair dryer has two settings: 1250 W and 1875 W.

(a) At which setting do you guess the resistance to be higher?

After making a guess, determine the resistance at

(b) the lower setting, and

(c) the higher setting.

(II) You buy a 75-W lightbulb in Europe, where electricity is delivered at 240 V. If you use the bulb in the United States at 120 V (assume its resistance does not change), how bright will it be relative to 75-W 120-V bulbs? [Hint: Assume roughly that brightness is proportional to power consumed.]

(II) At $0.12/kWh, what does it cost to leave a 25-W porch light on day and night for a year?

(II) A power station delivers 750 kW of power at 12,000 V to a factory through wires with total resistance 3.0 Ω. How much less power is wasted if the electricity is delivered at 50,000 V rather than 12,000 V?

(II) A traditional incandescent lamp filament may have been lit to a temperature of 2700 K. A contemporary halogen incandescent lamp filament may be at around 2900 K.

(a) Estimate the percent increase in efficiency of the halogen bulb over the traditional one. [Hint: See Section 19–10.]

(b) To produce the same amount of light as a traditional 100-W bulb, estimate what wattage a halogen bulb should use.

(III) A 1.0-m-long round tungsten wire is to reach a temperature of 3100 K when a current of 18.0 A flows through it. What diameter should the wire be? Assume the wire loses energy only by radiation (emissivity ∊ = 1.0 , Section 19–10) and the surrounding temperature is 20°C.

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

The current in an electromagnet connected to a 240-V line is 21.5 A. At what rate must cooling water pass over the coils for the water temperature to rise no more than 5.50 C°?

An 1875-W hair dryer is designed for 117 V.

(a) What will be the percentage change in power output if the voltage drops to 105 V? Assume no change in resistance.

(b) How would the actual change in resistivity with temperature affect your answer?

A microwave oven running at 72% efficiency delivers 950 W to the interior. Find

(a) the power drawn from the source, and

A microwave oven running at 72% efficiency delivers 950 W to the interior. Find

(b) the current drawn. Assume a source voltage of 120 V.

Determine the resistance of the tungsten filament in a 75-W 120-V incandescent lightbulb

(a) at its operating temperature of about 2800 K,

A 100-W, 120-V incandescent lightbulb has a resistance of 12 Ω when cold (20°C) and 150 Ω when on (hot). Calculate its power consumption

(a) at the instant it is turned on, and

(b) after a few moments when it is hot.

In an automobile, the system voltage varies from about 12 V when the car is off to about 13.8 V when the car is on and the car’s generator (or “alternator”) is in operation, a difference of 15%. By what percentage does the power delivered to the headlights vary as the voltage changes from 12 V to 13.8 V? Assume the headlight resistance remains constant.

Lightbulb A is rated at 120 V and 40 W for household applications. Lightbulb B is rated at 12 V and 40 W for automotive applications.

(a) What is the current through each bulb?

Lightbulb A is rated at 120 V and 40 W for household applications. Lightbulb B is rated at 12 V and 40 W for automotive applications.

(b) What is the resistance of each bulb?

If a wire of resistance R is stretched uniformly so that its length doubles, by what factor does the power dissipated in the wire change, assuming it remains hooked up to the same voltage source? Assume the wire’s volume and density remain constant.

An electric heater is used to heat a room of volume 65m³ . Air is brought into the room at 5°C and is completely replaced twice per hour. Heat loss through the walls amounts to approximately 750 kcal/h. If the air is to be maintained at 22°C, what minimum wattage must the heater have? (The specific heat of air is about 0.17 kcal/kg •C° .)

(II) A voltage V is applied to n identical resistors connected in parallel. If the resistors are instead all connected in series with the applied voltage, show that the power transformed is decreased by a factor n² .

A flashlight bulb rated at 2.0 W and 3.0 V is operated by a 9.0-V battery. To light the bulb at its rated voltage and power, a resistor R is connected in series as shown in Fig. 26–81. What value should the resistor have?

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In the circuit shown in Fig. 26–75, the 33-Ω resistor dissipates 0.80 W. What is the battery voltage?

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A 2800-W oven is connected to a 240-V source.

(b) How long will it take to bring 150 mL of 15°C water to 100°C assuming 65% efficiency?

Copper wire of diameter 0.259 cm is used to connect a set of appliances at 120 V, which draw 1250 W of power total.

(a) What power is wasted in 25.0 m of this wire?

A 2800-W oven is connected to a 240-V source.

(a) What is the resistance of the oven’s heating elements?

(II) A flashlight uses two AA 1.5-V batteries connected in series to provide 3.0 V across the bulb, as in Fig. 25–4b. The bulb draws 135 mA when turned on.

(a) Calculate the resistance of the bulb and the power dissipated.

(b) By what factor would the power increase if four AA batteries in series (total 6.0 V) were used with the same bulb? (Neglect heating effects of the filament.) Why shouldn’t you try this?

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The performance of the starter circuit in a car can be significantly degraded by a small amount of corrosion on a battery terminal. Figure 26–88a depicts a properly functioning circuit with a battery (12.5-V emf, 0.02-Ω internal resistance) attached via corrosion-free cables to a starter motor of resistance Rₛ = 0.15Ω . Sometime later, corrosion between a battery terminal and a starter cable introduces an extra series resistance of only R_C = 0.10Ω into the circuit as suggested in Fig. 26–88b. Let P₀ be the power delivered to the starter in the circuit free of corrosion, and let P be the power delivered to the starter with corrosion. Determine the ratio P/P₀ .

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