A heater is being designed that uses a coil of 14-gauge (1.628 mm diameter) platinum wire to generate 303 W using a voltage of V = 114 V. How long should the engineer make the wire (in m)?

l ength of wire =842.37m

Explanation:

Given that

Power generated, P= 303W

Voltage used, V = 114V

we will calculate the resistance of the wire first,

The  resistance of the wire will be  calculated from the equation

P= V²/R

R=  V²/P = (114)²/303= 42.89ohm

Also  Resistance = resistivity x length/ cross sectonal area

R=

where ρ= resistivity of  platinum =10.6 x 10^-8ohm meter

diameter platinum wire used, d = 1.628mm = 0.001628m

Therefore radius,= d/2 = 0.001628m/ 2=0.000814m

length of wire= R x A/ ρ

= R X π r²/ρ

L= 42.89 x 3.142 x(0.000814)²/10.6 x 10^-8ohm meter

=842.37m

amplitude

hope this

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