Cross-Sectional Area of a wire?
The rear window defogger of a particular car consists of 11 thin wires (resistivity = 1.07E-6 m) embedded in the glass. The wires are connected in parallel to the 12.0 V battery, and each has a length of 1.27 m. The defogger can melt 2.60E-2 kg of ice at 0°C into water at 0°C in two minutes. Assume that all the power delivered to the wires is used immediately to melt the ice. What is the cross-sectional area of the wire(m^2)?
The heat required to melt the ice
ΔQ = m·ΔHf
= 2.9×10-2kg · 333.55kJ
= 9672.95J
The electrical power delivered is
P= U·I
using Ohm's law (U = R·I)
you find
P= U² / R_t
where R_t is the total resistance of the defogger.
The electrical power is immediately used to melt the ice:
U²/R_t = ΔQ/Δt
<=>
Rt = U² ·Δt / ΔQ
= (12V)² · (120s) / 9672.95J
= 1.7864 Ω
The fogger consist of 14 parallel connected identical Resistances R:
So
1/R_t = Σ 1/R = 14/R
=>
R = 14·R_t
= 14 · 1.7864 Ω
= 25.01 Ω
The resistance of a single wire is:
R = ρ·L/A
ρ is the resistivity of the material
Hence:
A = ρ·L/R
= 1.08×10-6Ωm · 1.16m / 25.01Ω
= 1.08×10-6Ωm
= 5.01×10-8m²
= 0.0501mm²
Jujitsu Defense Techniques : Jujitsu: Parallel Wrist Grab Defense
 |
No items matching your keywords were found.