Question

A carbon resistor is 4 mm long and has a constant cross section of 0.2 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 12 volts relative to ground, and at the other end the potential is 16 volts. Calculate the resistance and the current .

Answer 1

Resistance (R) = 0.6667 ohm and Current (I) = 6A

Explanation: Please see the attachments below

Answer 2

The resistance is found to be 6Ω

The current is found to be 0.66 A

Step-by-step explanation:

The resistance of a conductor in terms of its dimensions is given as:

R = ρL/A

where,

R = resistance = ?

ρ = resistivity = 3 x 10⁴ Ω.m

L = Length = 4 mm = 0.004 m

A = Cross-sectional area = 0.2 mm² = 0.2 x 10⁻⁶ m²

Therefore,

R = (3 x 10⁴ Ω.m)(0.004 m)/(0.2 x 10⁻⁶ m²)

R = 6 Ω

Now, the potential difference between both ends of the resistor is:

ΔV = 16 V - 12 V = 4 V

Now, from Ohm's Law:

V = IR

I = V/R

I = 4 V/ 6 Ω

I = 0.66 A