Question

Chapter 27, Problem 012 The figure shows a resistor of resistance R = 6.32 ? connected to an ideal battery of emf 8 = 12.3 V by means of two copper wires. Each wire has length 23.0 cm and radius 1.90 mm. In dealing with such circuits in this chapter, we generally neglect the potential differences along the wires and the transfer of energy to thermal energy in them. Check the validity of this neglect for the circuit of the figure below. What is the potential difference across (a) the resistor and (b) each of the two sections of wire? At what rate is energy lost to thermal energy in (c) the resistor and (d) each section of wire? ire Wire 2 (a) Number (b) Number (c) Number (d) Number Units Units Units Units Click if vouu would like to Show Work for this question: Onen Show Work

Answer 1

Given,

E = 12.3 V ; R = 6.32 Ohm ; L = 23 m ; r = 1.9 mm ;

For each wire

R = rho L/A

R' = 1.69 x 10^-8 x 0.23/[3.14 x (1.9 x 10^-3)^2] = 3.43 x 10^-4 Ohm

The total resistance of the circuit will be:

Req = R + 2R' = 6.32 x 2 x 3.43 x 10^-4 = 6.32035 Ohm

I = E/Req = 12.3/6.3207 = 1.946 A

Vr = 1.946 x 6.32 = 12.29

Vw = 12.3 - 12.29 = 0.01 V

(a)V = 12.29 V

(b)V = 0.01 V

(c)P = I^2 R = 1.946^2 x 6.32 = 23.93 W

P = 23.93 W

(d)P = 1.964^2 x 3.43 x 10^-4 = 0.0013 W

P = 0.0013 W