Question

A carbon resistor is 4 mm long and has a constant cross section of 0.5 mm2. The conductivity of carbon at room temperature is 3 × 104 per ohm·m. In a circuit its potential at one end of the resistor is 11 volts relative to ground, and at the other end the potential is 14 volts. Calculate the resistance and the current .

Answer 1

R = 0.27 ohm

i = 11.25 A

Step-by-step explanation:

Resistance of a given cylindrical rod is

`R = \rho (L)/(A)`

here we know that

`\rho = (1)/(3 * 10^4) = 3.33 * 10^(-5) ohm-m`

Now we have

`R = (3.33 * 10^(-5))* (4 * 10^(-3))/(0.5 * 10^(-6))`

`R = 0.27 ohm`

now we know by ohm's law

`\Delta V = i R`

`14 - 11 = i ( 0.27)`

`i = 11.25 A`