Question

the total resistance of a 120v, two-wire circuit consisting of two no. 12 awg solid copper conductors, each 100' long is

Answer 1

To calculate the total resistance of a 120V, two-wire circuit consisting of two No. 12 AWG solid copper conductors, each 100 feet long, we can use the following formula:

R = (ρ * L) / A

where R is the resistance, ρ is the resistivity of the copper wire, L is the length of the wire, and A is the cross-sectional area of the wire.

The resistivity of copper is approximately 1.68 x 10^-8 ohm-meters at room temperature. The cross-sectional area of No. 12 AWG wire is 3.31 mm^2 (0.0051 in^2).

To convert the length from feet to meters, we can use the conversion factor 1 ft = 0.3048 m.

Now we can calculate the resistance of each wire:

R = (1.68 x 10^-8 ohm-meters * 100 ft * 0.3048 m/ft) / 3.31 mm^2 = 0.055 ohms

Since the circuit has two wires in parallel, the total resistance is:

R_total = R / 2 = 0.0275 ohms

Therefore, the total resistance of the circuit is 0.0275 ohms.

Answer 2

To calculate the total resistance of the circuit, we need to consider the resistance of each wire and the resistance of the entire circuit. The resistance of a wire can be determined using the formula:

Resistance (R) = (ρ * L) / A

where:

ρ is the resistivity of copper (approximately 1.68 x 10^-8 ohm-meter),

L is the length of the wire (in meters), and

A is the cross-sectional area of the wire (in square meters).

Since the length of each wire is given in feet, we need to convert it to meters:

100 feet = 30.48 meters (approximately).

Now, let's calculate the cross-sectional area (A) of a No. 12 AWG solid copper conductor. The AWG (American Wire Gauge) standard specifies the diameter of the wire, and the cross-sectional area can be calculated using the formula:

A (in square meters) = (π * d^2) / 4

where d is the diameter of the wire (in meters).

For No. 12 AWG, the diameter (d) is approximately 0.0808 meters.

Let's proceed with the calculations:

Calculate the cross-sectional area of the wire (A):

A = (π * (0.0808 meters)^2) / 4

A ≈ 0.002048 square meters

Calculate the resistance of each wire (R_wire):

R_wire = (ρ * L) / A

R_wire = (1.68 x 10^-8 ohm-meter * 30.48 meters) / 0.002048 square meters

R_wire ≈ 0.2518 ohms (approximately)

Since the circuit consists of two wires in series, add their resistances to get the total resistance (R_total):

R_total = R_wire + R_wire

R_total ≈ 0.2518 ohms + 0.2518 ohms

R_total ≈ 0.5036 ohms

So, the total resistance of the 120V, two-wire circuit is approximately 0.5036 ohms.