Question

What is the resistivity of a series of six 0.1 m square metal dice each of 1 ohm resistance made into a cuboid connected in a circuit through its smaller faces to a 12 V battery ? Also , calculate the current in the circuit and draw the circuit diagram . ​

Answer 1

$\sf Resistivity(\rho)= \frac{RA} {l} \\\\\sf </p><p>Since,~ the~ resistances ~are ~in ~series, \\\\\sf </p><p>The~length~ of ~each ~side ~of ~metal ~dice ~is~ 0.1m,~ \\\\\sf then ~if ~all~ the~ six~ are~ joined~ together, \\\\\sf ~the~ total~ length ~will~ be~ \\\\\sf 0.1 x 6 m =0.6m \\\\\sf </p><p>Hence, l= 0.6m \: R= 6 \Omega \: A= 0.1 m^2 \\\\\sf </p><p>So, the~ resistivity~ is ~\frac{RA} {l} \\\\\sf </p><p>= \frac{6x0.1} {0.6} \\\\\sf </p><p>= \frac{0.6}{0.6} \\\\\sf </p><p>= 1 \\\\\sf </p><p>Hence, the~ resistivity~ is~ 1 </p><p>$

Now, we know that V=IR

12= I x 6

I=2A