help with an equation please!

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mimi

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hello,
could anyone help with this question?

A 2.5mm square twin copper cable 20m long supplies a heating appliance having three elements each of resistance 57.6 ohms. If the elements are arranged such that two are in series and the third is in parallel with these two, calculate: (a) the resistance of the cable; and (b) the total resistance of the whole circuit. (p for copper is 17 x 10to the power of 6 ohms)?

I know the answers are (a) 0.272 ohms and (b) 38.672 ohms, I am just not sure how to get there, would be grateful for any insight?

thanks
 
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mpross

Senior Member
Location
midwest
Equation

Equation

mimi,

For the resistance R of the cable:

R = p*L / A

= ((17*10^-6)*40) / .0025 = .272 Ohms

For the resistance of the whole circuit:

The two resistors in series just add>> 57.6*2 = 115.2
...now for the parallel resistor: use the "product over sum" rule:
(115.2*57.6)/(115.2+57.6) = 38.4 Ohms

...38.4 + .272 = 38.672 Ohms

Hope this helps

-mpross
 
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mpross

Senior Member
Location
midwest
Resistance of wire

Resistance of wire

georgestolz,

I found the conductivity of Cu to be .596 x 10^6 / (cm Ohms). Conductivity is the inverse of resistivity. For a better explanation than what I could give in this forum, check out this site. It has a ton of good info!

http://230nsc1.phy-astr.gsu.edu/hbase/hframe.html

hyperphysics > Electricity and Magnetism > Resistor

Have fun with the site!

mpross
 
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