(a)
The relationship between the diameter and the length of the wire.
(a)
Answer to Problem 28P
The relationship between the diameter and the length of the wire is
Explanation of Solution
Write the expression for the output power of the heater.
Here,
Write the expression for the
Here,
Use equation (II) in (I) to solve for
Write the expression for power relating the resistance.
Here,
Use equation (IV) to solve for
Write the expression for the resistivity.
Here,
Write the expression for resistance.
Here,
Write the expression for
Here,
Use equation (VIII) in (VII) to solve for
Use the unit conversion
Conclusion:
Substitute
Substitute
Substitute
Substitute
Therefore, the relationship between the diameter and the length of the wire is
(b)
The volume of the nichrome wire is less than
(b)
Answer to Problem 28P
Explanation of Solution
Write the expression for the volume.
Here,
Use equation (VIII) in (X) to solve for
Use the relation obtained from part (a),
Use equation (XII) in (XI) to solve for
Use equation (XIII) in (XII) to solve for
Conclusion:
Substitute
Substitute
Therefore, the volume
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Chapter 21 Solutions
Bundle: Principles of Physics: A Calculus-Based Text, 5th + WebAssign Printed Access Card for Serway/Jewett's Principles of Physics: A Calculus-Based Text, 5th Edition, Multi-Term
- A 12.0-V emf automobile battery has a terminal voltage of 16.0 V when being charged by a current of 10.0 A. (a) What is the battery’s internal resistance? (b) What power is dissipated inside the battery? (c) At what rate (in °C/min ) will its temperature increase if its mass is 20.0 kg and it has a specific heat of 0.300 kcal/kg • °C, assuming no heat escapes?arrow_forwardAn office worker uses an immersion heater to warm 250 g of water in a light, covered, insulated cup from 20.0°C to 100°C in 4.00 min. The heater is a Nichrome resistance wire connected to a 120-V power supply. Assume the wire is at 1008C throughout the 4.00-min time interval. (a) Specify a relationship between a diameter and a length that the wire can have. (b) Can it be made from less than 0.500 cm3 of Nichrome?arrow_forwardElectrical energy is converted to heat at the rate of 7.56kJ/min in a resistor which has 270 C/min passing through. What is the voltage difference across the resistor terminals?arrow_forward
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- An immersion-type heating coil with a resistance of 13 ohms is connected to a 120 V outlet and immersed in a 250 mL cup of water initially at 10 degree Celsius. Assume that there is no heat loss and neglect the heater's heat capacity. How long does it take to bring the water to the boiling point?arrow_forwardAn uncharged capacitor and a resistor are connected in series to a battery as shown in Figure, where e= 12.0 V, C = 5.00 mF, and R = 8.00 × 105 W. The switch is thrown to position a. Find the time constant of the circuit, the maximum charge on the capacitor, the maximum current in the circuit, and the charge and current as functions of time.arrow_forwardA 660 W electric heater is designed to operate from a 120 V source. If the source voltage drops to 80.0 V, what will be the power dissipated by the same heater? (Assume the resistance of the heater is constant.) a. 440 W b. 660 W c. 293 W d. 73.3 Warrow_forward
- A copper wire is dCu = 0.0500 cm in diameter, 3.00 m long, and has a charge carrier density of 8.50x10^28 electrons/m3. The copper wire is attached to an equal length of aluminum wire with diameter dAl = 0.0100 cm and charge carrier density of 6.02x10^28 electrons/m3. A current of 0.400 A flows through the copper wire. a. The ratio of current densities in the two wires, JCu/JAl is:___. b. The ratio of drift velocities in the two wires, vd–Cu/vd–Al is:____.arrow_forwardConsider current passing through a rectangular resistor (below) in two scenarios: along the length of the resistor (A) and across the width of the resistor (B). The dimensions of the resistor are: length (R = 10 cm); width (R’ = 5 cm), and height (h = 2 cm). The resistivity of the rectangular resistor is constant throughout. Which of the following statements are true? Choose the best answer. a. The resistance in (A) is 4x the resistance in (B) b. The resistance in (A) is 2x the resistance in (B) c. The resistance in (A) is ½ the resistance in (B) d. The resistance in (A) is ¼ the resistance in (B) e. The resistances in (A) and (B) are equalarrow_forwardWhat current (in A) must be produced by a 12.0 V battery-operated bottle warmer in order to heat 74.0 g of glass, 300 g of baby formula, and 2.50 ✕ 102 g of aluminum from 20.0°C to 90.0°C in 4.50 min? (Assume the specific heats of glass, baby formula, and aluminum are 840 J/(kg · °C), 4,186 J/(kg · °C), and 900 J/(kg · °C), respectively.) Aarrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning