It is necessary to double the length of a wire, but the resistance of the wire...

It is necessary to double the length of a wire, but the resistance of the wire needs to remain APPROXIMATELY the same. If the wire is initially 22 gauge, what gauge of wire should be used to accomplish this?

Expert Solution

Resistance, R = ( * L) / A ...(1)
Where is the resistivity of the wire, L is the length of the wire and A is the area of the wire.

L becomes 2L but resistance remains the same
R = ( * 2L) / Anew ...(2)
Where Anew is the new area of the wire

(1) / (2) gives
1 = Anew / (2 * A)
2 = Anew / A
2 = Rnew2 / R2
Where Rnew and R are the radius of the new and old wire respectively.
2 = (Rnew/R)2
Taking square root on both the sides,
= Rnew/R
Rnew = 1.414 * R
Dnew = 1.414 * D
Where Dnew is the diameter of the new wire and D is the diameter of the old wire

According to American wire gauge system, 22 gauge corresponding to a diameter of 0.644 mm
Diameter of new wire, Dnew = 0.644 * 1.414
= 0.911 mm
This corresponds to 19 gauge wire

genius_generous answered 2 years ago

The electrical resistance of a wire varies directly as its length and inversely as the square...

The electrical resistance of a wire varies directly as its length and inversely as the square of its diameter. A wire with a length of 200 inches and a diameter of one-half of an inch has a resistance of 10 ohms. Find the electrical resistance in a 500 inch wire with the same diameter. Group of answer choices 25 ohms 50 ohms 200 ohms 400 ohms

What is the resistance of a 2.9-m length of copper wire 1.4 mm in diameter?

What is the resistance of a 2.9-m length of copper wire 1.4 mm in diameter? The resistivity of copper is 1.68×10-8Ω⋅m.

A square wire loop of side length a = 2.0 cm and resistance R = 10.0Ω...

A square wire loop of side length a = 2.0 cm and resistance R = 10.0Ω is inside a 1.00m long solenoid with 1000 windings such that the plane of the loop is perpendicular to the solenoid’s magnetic field. The solenoid initially carries a current I = 6.0 A, which is turned down to zero evenly over a period of 12.0 s. If the solenoid’s initial magnetic field is out of the page in the figure, what is the magnitude...

A given copper wire has a resistance of 5.10 ? at 20.0°C while a tungsten wire...

A given copper wire has a resistance of 5.10 ? at 20.0°C while a tungsten wire of the same diameter has a resistance of 4.67 ? at 20.0°C. At what temperature will the two wires have the same resistance?

a) A cylindrical length of wire has a radius of 4 mm and a length of...

a) A cylindrical length of wire has a radius of 4 mm and a length of 10 cm. If the length is growing at a rate of 2 cm/sec and the radius is shrinking at a rate of 1 mm/sec, what is the rate of change of the volume in cm3/sec at that point in time. (Be careful of units) b) Consider the same length of wire as before (radius of 4 mm and length of 10 cm). This time...

double maxArea(Rectangle a, Rectangle b, Rectangle c) { double width; double length; double...

double maxArea(Rectangle a, Rectangle b, Rectangle c) { double width; double length; double area = 0; area = width * length; cout << "\n***maxArea called" << endl; cout << "*** rectangleCount = " << Rectangle::rectangleCount << endl << endl; } Compete this code to find the maximum area of rectangle between a,b,c

Consider two long wire with negligible resistance closed at one end of the resistance R (say...

Consider two long wire with negligible resistance closed at one end of the resistance R (say a light bulb), and the other end connected to a battery (DC voltage). Cross-sectional radius of each wire is in x=100 times smaller than the distance between the axes of the wires. Question: At which value of resistance R (in ohms) the resultant force of the interaction of parallel conductors disappears?

The resistance R of a tungsten wire as a function of temperature can be modeled with...

The resistance R of a tungsten wire as a function of temperature can be modeled with the equation R=R0*[1+α(T-T0 ) whereR0 is the resistance corresponding to temperature T0, and α is the temperaturecoefficient of resistance. Determine R0and α such that the equation will best fit the following data (Use linear regression curve fitting). Take T0 = 20°C. T=[20 100 180 260 340 420 500] R=[500 676 870 1060 1205 1410 1565] After enter below codes it gives an error function...

A wire loop has an area of 0.36 m2 and a resistance of 1.5 ?. The...

A wire loop has an area of 0.36 m2 and a resistance of 1.5 ?. The loop lies in a horizontal plane where there is a downward-directed magnetic field of magnitude 0.015 T. The wire is pulled to one side so that it is completely out of the field after 0.20 s. For the 0.20-s period during which the loop is being pulled out of the magnetic field, find the following: a. Find the average induced emf in the loop....

1-What four physical factors affect the resistance of a wire? 2-A wire of uniform cross-section has...

1-What four physical factors affect the resistance of a wire? 2-A wire of uniform cross-section has a resistance of R. What would be the resistance of a similar wire, made of the same material, but twice as long and of twice the diameter? 3- A block of carbon, 1.0 cm by 2.0 cm by 5.0 cm, has a resistance of 0.015 Ω between its two smaller faces. What is the resistivity of carbon? 4-What length of German silver wire, diameter...

Question