What length of German silver wire, diameter 0.050 cm, is needed to make a 28 Ωresistor, if the resistivity of German silver is 2.2 × 〖10〗^(-7) Ω m
(show work)
Given :
Resistance R = 28Ω
A is the cross-section area and, ρ is resistivity of the wire.
To find length l
A=π(0.00025)
2
㎡=625π×10 −10
28=2.2×10 −7
So, l=28×625π×10
−3
/2.2=24.98=25m
To find the length of the German silver wire needed to make a 28 Ω resistor, we can use the formula:
Resistance (R) = resistivity (ρ) x length (L) / cross-sectional area (A)
In our case, the cross-sectional area can be calculated using the formula:
Area (A) = π x (diameter/2)^2
Given:
Resistance (R) = 28 Ω
Resistivity (ρ) = 2.2 × 10^(-7) Ω m
Diameter (d) = 0.050 cm = 0.0005 m
First, let's calculate the cross-sectional area:
A = π x (0.0005/2)^2
= π x 0.00025^2
= π x 6.25 x 10^(-8) m^2
= 1.962 x 10^(-7) m^2
Now, we can rearrange the resistance formula to solve for the length:
L = (R x A) / ρ
L = (28 x 1.962 x 10^(-7)) / (2.2 x 10^(-7))
L = 54.536 x 10^(-7) m
L = 5.4536 cm
Therefore, a German silver wire with a length of approximately 5.4536 cm is needed to make a 28 Ω resistor.
To determine the length of German silver wire needed to make a 28 Ω resistor, we can use the formula for the resistance of a wire:
R = ρ * (L / A),
Where:
R is the resistance of the wire,
ρ is the resistivity of the material (German silver in this case),
L is the length of the wire, and
A is the cross-sectional area of the wire.
In this case, we are given the resistance R and the resistivity ρ. We need to find the length L.
First, let's find the cross-sectional area A of the wire. The formula for the area of a circle is given by:
A = π * r^2,
Where:
A is the area,
π is a mathematical constant (approximately 3.14159), and
r is the radius of the wire.
We are given the diameter of the wire, which is 0.050 cm. To find the radius, divide the diameter by 2:
r = 0.050 cm / 2 = 0.025 cm.
Now, let's convert the radius to meters:
r = 0.025 cm * (1 m / 100 cm) = 0.00025 m.
Using this value, we can find the cross-sectional area A:
A = π * (0.00025 m)^2 = 1.96 × 10^(-7) m^2.
Now, we can rearrange the resistance formula to solve for the length L:
L = (R * A) / ρ.
Substituting the given values:
L = (28 Ω * 1.96 × 10^(-7) m^2) / (2.2 × 10^(-7) Ω m).
Calculating:
L = 25.27 m.
Therefore, a length of approximately 25.27 meters of German silver wire with a diameter of 0.050 cm is needed to make a 28 Ω resistor.