Question

You have two wires connected end-to-end (in series). Wire 1 is copper and wire 2 is made from a "special" carbon conductor. Wire 1 has a resistance of 0.215 Ω/ft. and is 500 ft. long. Wire 2 has a resistance of 0.141 Ω/ft. and is 700 ft. long. Both of these resistances are measured at 20°C. If the ambient temperature is 99°F, what is the wire’s total series resistance? (FROM AN OLD F.E. EXAM) A reminder that temperatures must be first converted to Celsius or Kelvin

Answer 1

212.66Ω

Step-by-step explanation:

the temperature coefficient of resistance is normally standardized in relation to a temperature of 20°C.

R = Rref(1+ ∝(T-Tref))

R = R₂₀(1+ ∝₂₀(T-20))

R= resistance at temperature T

Rref = the resistance at temperature Tref

∝= temperature coefficient of resistance for the material

T= material temperature in celsius

Tref = reference temperature for which the temperature coefficient is specified.

∝ for copper=0.00393/°C

∝ for carbon = -0.00048/°C

Wire 1 resistance at 20°C

length = 500ft

R= 0.215×500= 107.5Ω

wire 2 resistance at 20°C

R = 0.141×700= 98.7Ω

converting 99°F to °C

°C = 5/9(°F- 32)

°C = 37.22Ω

R = R₂₀(1+ ∝₂₀(T-20))

R= 107.5 (1+ 0.00393(37.22-20))

R = 114.78Ω ; resistance of copper

R = 98.7 (1+ (-0.00048(37.22-20)))

R= 97.88Ω

Total resistance = 97.88 + 114.78

R(total)=212.66Ω