Question

4a. The resistance of a 5.0 meter length of 14-gauge copper wire is 8.1 x 10 ohms/meter. How much energy loss occurs per second in the wire when a current of 20.0 amps is applied? Assume that the cross-sectional area is 2.1 mm', what is the shortest time in which the applied current could heat the wire by 15.0°C? You may assume that the density of copper is 8.92 x 10 kg/m and its molar heat capacity is 6.0 calories/mole/K.

Answer 1

4 a )

given

m = 8.1 x 10^-3 ohms/meter

R = 8.1 x 10^-3 x 5 ( for 5 Ohm )

R = 40.5 x 10^-3 ohms/meter

a )

P = i² R

= 20 x 20 x 40.5 x 10^-3

P = 16.2 W

m = $\rho$ V

= 8.92 x 10³ x 5 x 2.1 x 10^-3

= 93.66 kg

no of moles = 93.66 x 1000 / 63.5

= 1474.9601 moles

Q = 1474.96 x 6 x 15

Q = 555676.43 J

time = 555676.43 / 16.2

t = 34301.33 sec

4 b )

given

d = 2.5 mm

= 2.5 x 10^-3 m

r = 15 cm

= 0.15 m

V = 1000 volts

Q = C V

= $\varepsilon$ _o A V / d

= 8.85 x 10^-12 x 3.14 x 0.15² x 1000 / 2.5 x 10^-3

Q = 2.501 x 10^-7 C

= 0.2501 x 10^-6 C

so the charge stored on the capacitor is Q = 0.2501 $\mu$ C