The rear window defogger of a car consists of thirteen thin wires (resistivity =

Question

The rear window defogger of a car consists of thirteen thin wires (resistivity = 117 Times 10^-8 Ohm-m) embedded in the glass. The wires are connected in parallel to the 12.0-V battery, and each has a length of 1.26 m. The defogger can melt 0.0200 kg of ice at 0 degree C into water at 0 degree C in two minutes. Assume that all the power dissipated in the wires is used immediately to melt the ice. Find the cross-sectional area of each wire. Take the latent heat of fusion of water to be 3.35 Times 10^5 J/kg.

Explanation / Answer

power supplied by each wire = 12^2 /R

total = (12^2 /R) *13

R= row * L /A

=117*10^-8 *1.26/A

now energy required for melting = 3.35 *10^5 *0.0200 *2*60

=804000 J

so

144 *A /(117*10^-8 *1.26) = 804000

A = 804000 *(117*10^-8 *1.26 ) /144

=0.00823095 m2

=82.30 square cm

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