The average resistance of the project
Question 1
a) 600 m of wire is allocated for 5 houses. Only 450 m is delivered. How many houses can be wired completely?
b) Two thirds of a project is wired using wire with resistance of. The remaining third uses wire of . What is the average resistance of the project?
c) What would the resistance be if the project in b) used 50 m of wire?
d) What would the length of each wire type be in b)?
Question 2
Using Mesh Analysis for the circuit shown, the following two equations are obtained for the currents. Solve them simultaneously, showing your chosen method. Values to 3 s.f.
Question 3
What is the voltage drop over two 12 AWG conductors (resistance of 0.20 ohms per 100 m) supplying a 16 A load located 50 m from the power supply?
Question 1:
a) To determine how many houses can be wired completely with 450 m of wire out of the allocated 600 m, we need to find the amount of wire used per house.
Wire used per house = Total wire allocated / Number of houses Wire used per house = 600 m / 5 houses = 120 m per house
Since only 450 m of wire is delivered, we can wire a maximum of:
Number of houses that can be wired completely = Wire delivered / Wire used per house Number of houses that can be wired completely = 450 m / 120 m per house = 3.75 houses
Since we cannot wire a fraction of a house, we can conclude that 3 houses can be wired completely with 450 m of wire.
b) To find the average resistance of the project with two-thirds wired using wire with resistance “a” and one-third wired using wire with resistance “b,” we can use the formula for the average resistance of resistors in parallel:
Average resistance = (Resistance of a * Resistance of b) / (Resistance of a + Resistance of b)
c) If the project in question b) used 50 m of wire, we need to calculate the new average resistance. We can use the same formula as in question b) to find the average resistance with the given length of wire.
d) To determine the length of each wire type in question b), we need to calculate the length of wire used for two-thirds of the project and one-third of the project separately. We can use the following formulas to find the lengths:
Length of wire with resistance “a” = Total wire length * (2/3) Length of wire with resistance “b” = Total wire length * (1/3)
Question 2:
Unfortunately, you have not provided the circuit or the equations obtained from Mesh Analysis. Please provide the necessary information or equations to solve this question.
Question 3:
To find the voltage drop over two 12 AWG conductors supplying a 16 A load located 50 m from the power supply, we need to calculate the resistance of the conductors and then use Ohm’s Law.
Resistance of two 12 AWG conductors = Resistance per 100 m * Length in meters / 100 Resistance of two 12 AWG conductors = 0.20 ohms per 100 m * 50 m / 100 = 0.10 ohms
Using Ohm’s Law: Voltage drop = Current * Resistance
Voltage drop = 16 A * 0.10 ohms = 1.6 volts
Therefore, the voltage drop over two 12 AWG conductors supplying a 16 A load located 50 m from the power supply is 1.6 volts.