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Unformatted text preview: Electrical energy is converted to heat at a rate given by P = V 2 / R, where V is the
potential difference across the heater and R is the resistance of the heater. Thus, 1050 CHAPTER 26 (120 V) 2
.
.
P=
= 10 × 103 W = 10 kW.
14 Ω
(b) The cost is given by (1.0kW)(5.0h)(5.0cents/kW ⋅ h) = US$0.25.
42. (a) Referring to Fig. 2632, the electric field would point down (toward the bottom of
the page) in the strip, which means the current density vector would point down, too (by
Eq. 2611). This implies (since electrons are negatively charged) that the conduction
electrons would be “drifting” upward in the strip.
(b) Equation 246 immediately gives 12 eV, or (using e = 1.60 × 10−19 C) 1.9 × 10−18 J for
the work done by the field (which equals, in magnitude, the potential energy change of
the electron).
(c) Since the electrons don’t (on average) gain kinetic energy as a result of this work done,
it is generally dissipated as heat. The answer is as in part (b): 12 eV or 1.9 × 10−18 J.
43. The relation P = V 2/R implies P ∝ V 2. Consequently, the power dissipated in the
second case is F 150 V IJ (0.540 W) = 0135 W.
.
.
P=G
H 3.00 V K
2 44. Since P = iV, the charge is
q = it = Pt/V = (7.0 W) (5.0 h) (3600 s/h)/9.0 V = 1.4 × 104 C. 45. (a) The power dissipated, the current in the heater, and the potential difference across
the heater are related by P = iV. Therefore,
i= P 1250 W
=
= 10.9 A.
115 V
V (b) Ohm’s law states V = iR, where R is the resistance of the heater. Thus,
R= V 115 V
=
= 10.6 Ω.
i 10.9 A (c) The thermal energy E generated by the heater in time t = 1.0 h = 3600 s is
E = Pt = (1250W)(3600s) = 4.50 ×106 J. 46. (a) Using Table 261 and Eq. 2610 (or Eq. 2611), we have 1051
⎛
⎞
2.00A
 E  = ρ  J  = (1.69 ×10−8 Ω⋅ m ) ⎜
= 1.69 ×10−2 V/m.
−6
2⎟
2.00 ×10 m ⎠
⎝ (b) Using L = 4.0 m, the resistance is found from Eq. 2616:
R = ρL/A = 0.0338 Ω. The rate of thermal energy generation is found from Eq. 2627:
P = i2 R = (2.00 A)2(0.0338...
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This document was uploaded on 02/26/2014 for the course PHYS 2b at UCSD.
 Fall '08
 schuller
 Magnetism, Work

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