Wires in an circuit, different materials, heat

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SUMMARY

The discussion focuses on calculating the cross-sectional area of a lead fuse wire (Sl=x) in an electric circuit with copper wires. Given parameters include a copper wire cross-section area of Sc=5mm², a temperature increase (Δt) of 25°C, and specific heat values for copper (cc=400J/kg°C) and lead (cl=140J/kg°C). The melting point of lead is 327°C, with a latent heat (λ) of 25000J/kg. The specific electrical resistances are ρc=0.017×10-6Ωm for copper and ρl=0.21×10-6Ωm for lead, which are crucial for solving the problem using the equations provided.

PREREQUISITES
  • Understanding of thermal energy equations: Q=cmΔt and Q=λm
  • Knowledge of electrical resistance calculations: R=lρ/S
  • Familiarity with material properties, including specific heat and melting points
  • Basic principles of electric circuits and heat transfer
NEXT STEPS
  • Research the relationship between temperature, specific heat, and mass in thermal calculations
  • Study the derivation and application of the latent heat equation in phase changes
  • Explore the impact of cross-sectional area on electrical resistance in circuits
  • Learn about the thermal properties of different materials, focusing on copper and lead
USEFUL FOR

This discussion is beneficial for students in physics or engineering, particularly those studying electrical circuits, thermal dynamics, and material science. It is also useful for anyone involved in designing safety mechanisms in electrical systems.

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Homework Statement


In an electric circuit, consisting of copper wires with cross section area of Sc=5mm2 and a temperature of t=25C, a lead fuse is added melting when the copper wire temperature increases by Δt=25C. Find the cross section area of the lead fuse wire Sl=x.
specific heat: cc=400J/kg*C cl=140J/kg*C.
Lead melting point tl=327C, latent heat λ=25000J/kg.
Specific electrical resistances of the materials: ρc=0,017*10-6Ωm, ρl=0,21*10-6Ωm.
material density: ρc1=8,9*103kg/m3, ρl1=11,34*103kg/m3.

Homework Equations


Q=cmΔt
Q=λm
R=lρ/S

Thank you for any ideas on how to solve this, if there is something confusing please ask, this equation is translated from a different language so there may be inaccuracies and such.
 
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Don't erase the part 3. Attempt at solution. We can't help if you don't post that...
 
I was asking for ideas, directions to try going towards, I'm not asking people to solve it. Anyway, I was thinking about Q1=Q2 Q1=ccm1Δt Q2=cl(tl-t). But I don't know the masses nor anything derivative from it since I need to find the cross section area.
 

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