While remodeling your garage, you need to temporarily splice, endto end, an 80 m
ID: 1751716 • Letter: W
Question
While remodeling your garage, you need to temporarily splice, endto end, an 80 m long copper wire that is 1.05mm in diameter with a 49 m long iron wire that hasthe same diameter. The maximum current in the wires is 2.00 A. (a) Find the potential drop across each wire of this system whenthe current is 1.95 A.V(copper wire)
V(iron wire)
(b) Find the electric field in each wire when the currentis 1.95 A.
mV/m(copper wire)
mV/m(iron wire) (a) Find the potential drop across each wire of this system whenthe current is 1.95 A.
V(copper wire)
V(iron wire)
(b) Find the electric field in each wire when the currentis 1.95 A.
mV/m(copper wire)
mV/m(iron wire)
Explanation / Answer
a) You could think of this problem as being a simplecircuit with two resistors in series, one resistor being the copperwire and the other being the iron wire. You are given thelength and diameter of the wires, so you can calculate theresistances using: R = (l * ) / A with l being the length, the electrical resistivitygiven in ohm-meters, and A being the cross-sectional area in squaremeters. So the cross sectional area for both cables is =r2 = (.0015m)2 =7.069x10-6m2 For copper:R = (80m * 1.72x10-8m) /(7.069x10-6m2) R = .195 For iron: R = (49m * 1.0x10-7m) /(7.069x10-6m2) R =.693 Now we use Ohm's Law to find the voltage drops: For copper: V = IR = (1.95A)(.195) = .380V For iron: V = IR = (1.95A)(.693) = 1.35V b) The electric field is simply the voltage drop divided by thelength of wire. So for copper: .380V / 80m = .00475 V/m = 4.75mV/m For iron: 1.35V / 49m = .02755 V/m = 27.55mV/m *Note: I got my values for from a table Ihave. If yours are slightly different due to rounding, thensubstitute your values in and follow my work to come up with moreexact solutions for your given data. *Note: I got my values for from a table Ihave. If yours are slightly different due to rounding, thensubstitute your values in and follow my work to come up with moreexact solutions for your given data.
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