A gold wire 5.90m long and of diameter 0.890 mm carries a current of 1.21A.
A)Find the resistance of this wire.
B)Find the potential difference between its ends.
Can someone please help me I don't know how to answer these questions?
R=p(L/A) 1.21(5.90m/.890mm)
Am i setting this up right?
A) You will have to use the resistivity of gold (which you should look up) to get an answer. The current makes no difference.
R = (rho)* (L/A) is the correct formula.
Make sure you use consistent units, such as ohm-cm for rho, cm for length, and cm^2 for area. You did not do that in what you wrote.
B)Once you have computed R, V = I R
Yes, you're on the right track. To find the resistance of the wire, you can use Ohm's Law. Ohm's Law states that the resistance (R) is equal to the product of resistivity (p), length (L), and the inverse of cross-sectional area (A). The formula is given as:
R = p(L / A)
Let's calculate the values step by step:
To find the resistance, you need to know the resistivity of gold. The resistivity of gold is typically around 2.44 x 10^-8 ohm*m (Ω*m).
Now, convert the diameter of the wire to meters:
Diameter = 0.890 mm = 0.890 x 10^-3 m
The radius (r) can be found by dividing the diameter by 2:
Radius = 0.890 x 10^-3 m / 2 = 0.445 x 10^-3 m
Next, calculate the cross-sectional area (A) of the wire using the formula for the area of a circle:
A = πr^2
Substitute the value of the radius:
A = π(0.445 x 10^-3 m)^2
Next, calculate the length (L) of the wire:
L = 5.90 m
Now, substitute the values into the formula for resistance:
R = p(L / A)
R = (2.44 x 10^-8 Ω*m)(5.90 m) / [π(0.445 x 10^-3 m)^2]
Simplify the expression and calculate the numerical value to find the resistance of the wire.
To find the potential difference between the ends of the wire, you can use Ohm's Law again:
V = I * R
Substitute the given current (I = 1.21 A) and the resistance (R) that you calculated earlier into the formula to find the potential difference (V) between the ends of the wire.