Residential building codes typically require the use of 12-gauge copper wire (di

Question

Residential building codes typically require the use of 12-gauge copper wire (diameter 0.205 cm) for wiring receptacles. Such circuits carry currents as large as 20.0 A. If a wire of smaller diameter (with a higher gauge number) carried that much current, the wire could rise to a high temperature and cause a fire. (Table of resistivities)

(a) Calculate the rate at which internal energy is produced in 1.70 m of 12-gauge copper wire carrying 20.0 A.
  W

(b) Repeat the calculation for a 12-gauge aluminum wire.
W

Explanation / Answer

here,

Resistance R = rho L/A

rho of copper = 1.67 *10^-8 ohm/m

R = 1.67 *10^-8 * 1.7*4/(3.14 * 0.00205 * 0.00205)

R = 0.0086 ohms

rate of internal energy P = i^2*R

Pi = 20*20 * 0.0086

Pi = 3.44 Watts

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for aluminium , rho = 2.65 *10^-8

so

rho = (2.65*10^-8* 1.7*4)/(3.14 * 0.00205* 0.00205)

rho = 0.013 ohm/m

Power Pi = i^2R =

Pi = 20*20 * 0.013

Pi = 5.2 watts

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