# 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?

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

Mar 16, 2018

Good one . See below

#### Explanation:

Firstly Resistance in milli ohmsof a material is:

$R = \rho \cdot \left(\frac{l}{A}\right)$

where
$\rho$ is the resitivity in millohms.meter
$l$ length in meters
$A$ Cross sectinal arae in ${m}^{2}$

$R = \rho \cdot \left(\frac{l}{A}\right) = 6.5 \cdot {10}^{-} 5 \cdot \frac{0.023}{{0.021}^{2}} = 7.2 \cdot {10}^{-} 3$ milliohms
$\frac{8.7}{7.2 \cdot {10}^{-} 3} = 1200$ Amps, the carbon block will burn out to maybe just air between the electrodes with a flash.