Solve Gold Ring Resistivity Question, Practical Difficulties

[TheOne123]

I was doing some questions from a book on resistivity and I came across this, I really can't work this out, I'm stumped.

In a resistance experiment, a gold ring as connected into a circuit as a resistor. The connections touched on a diametrically opposite points on the circular ring. Its diameter is 2CM, and the metal's cross-section is a rectangle 3mm by 0.5mm. A volt meter is connected across the ring measured 8.3 m V, whilst the current though it was measured at 18 A.

a) Calculate the resistivity of gold.
b) Describe a practical difficulty with undertaking an experiment of this kind.

 

[nasu]

You can consider two half-rings connected in parallel. For each one use the formula for the resistance of a wire.

 

[Andrew Mason]

I was doing some questions from a book on resistivity and I came across this, I really can't work this out, I'm stumped.

Calculate the resistance of the ring in this circuit. Then work out the resistance of one half of the ring on the basis that the two halves of the ring amount to two half rings in parallel. Then work out the resistivity from that resistance.

AM

 

[TheOne123]

Hmm ok. I'm still a bit cofused. Can someone start. Of te calculation for me please an I will go from there. Thanks in advance.

 

[ideasrule]

As for practical difficulties, how many gold rings have you seen that have a perfectly rectangular cross-section?

 

[Andrew Mason]

Hmm ok. I'm still a bit cofused. Can someone start. Of te calculation for me please an I will go from there. Thanks in advance.

Use Ohm's law to determine the resistance.

Since this total resistance is from two sides of the ring in parallel, you can work out the resistance of each side of the ring:

$$\frac{1}{R} = \frac{1}{R_{half}} + \frac{1}{R_{half}}$$

Use $\rho L/A = R$ to find the resistivity, where L is the length of the conductor and A is the cross sectional area.

AM

 

[TheOne123]

Ahh I still keep getting it wrong.

The answer should be 4.4 X 10^-7 as it says in the back.

 

[nasu]

Ahh I still keep getting it wrong.

The answer should be 4.4 X 10^-7 as it says in the back.

Isn't 4.4 X 10^-8?
This is more realistic.

 

[TheOne123]

Isn't 4.4 X 10^-8?
This is more realistic.

It says 4.4 X 10^-7. How did you get 4.4 X 10^-7?

 

[nasu]

If you show your work I'll try to identify the mistake.
But I think you'll get about 4x10^(-8).