Question

a rectangular resistor of length and cross-sectional area is connected to a battery as shown above. the resistor draws a current density equal to . if the resistivity of the resistor is , what is the potential difference of the battery?

Answer 1

The potential difference of the battery, given that the resistor draws a current density equal to 2500 A/m², is 12 V (option E)

How to calculate the potential difference of the battery?

First, we shall obtain the current drawn from the battery. This is shown below:

• Current density = 2500 A/m²
• Area = 8.0 cm² = 8 / 10000 = 0.0008 m²
• Current = ?

Current = Current density × Area

= 2500 × 0.0008

= 2 A

Next, we shall obtain the resistance of the resistor. This is shown below:

• Length (L) = 10 cm = 10 / 100 = 0.1 m
• Area (A) = 0.0008 m²
• Resistivity (ρ) = 0.048 Ωm
• Resistance (R) =?

`R = (\rho L)/(A) \\\\R = (0.048\ *\ 0.1)/(0.0008) \\\\R = 6\ \Omega`

Finally, we shall calculate the potential difference of the battery. Details below:

• Current (I) = 2 A
• Resistance (R) = 6 Ω
• Potential difference (V) = ?

V = IR

V = 2 × 6

V = 12 V

Thus, the correct answer is option E

Complete question:

See attached photo