14-gauge copper wire has a cross sectional area of 2.08x10 -6 m 2 and a resistiv
ID: 1391466 • Letter: 1
Question
14-gauge copper wire has a cross sectional area of 2.08x10-6m2 and a resistivity of 1.72x10-8 ohm meters.
*A particular device uses 176 m of this wired exposed to the maximum current, find the resistance of this length of wire & How much current will the whole system draw if this wire feeds a complex parallel circuit with an equivalent resistance of 3.62 ohms that is run using ordinary 120 V household voltage & Find the power consumed by the whole circuit & How much of that power will be used (dissipated, wasted) just in the wires?
Explanation / Answer
The resistance of the wire is,
R = resistivity ( L/A)
= 1.72x10-8 ohm meters. ( 176 m/2.08x10-6m2)
=1455.38 * 10 ^-3 ohm
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from the Ohm's law, the current in the circuit is
I = V/R = 120 V/ 3.62 ohm = 33.14 A
The power consumed by the whole is
P = VI = 120 V ( 33.14 A) = 3976.8 W
the disspated power in the wire
Q = I^2 Rt
Q/t = I^2 R
P = I^2 R = ( 33.14 A)^2 ( 3.62 ohm) = 36396.3W
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