A block of carbon is 2.3 cm long and has a square cross-sectional area with sides of 2.1 cm . A potential difference 8.7 V is maintained across its length. What is the resistance of the resistor?

Question

The resistivity of carbon is 6.5 × 10−5 Ω · m .
Answer in units of mΩ

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Answer 1 · 2018-03-16T23:11:43

Good one . See below

Firstly Resistance in milli ohmsof a material is:

#R= rho * (l/A)#

where
#rho# is the resitivity in millohms.meter
#l# length in meters
#A# Cross sectinal arae in #m^2#

In your case you have:

#R= rho * (l/A) = 6.5 * 10^-5 * 0.023/(0.021^2) =7.2*10^-3# milliohms

This would be the case if there was no current flow.

Applying the voltage causes a 8.7V . means there is current of:

#8.7/(7.2*10^-3) = 1200# Amps, the carbon block will burn out to maybe just air between the electrodes with a flash.