Physics 2021 JAMB Past Questions - Question 12: Calculate the time required to electroplate a substance of area 300cm² with a layer of copper 0.6mm thick, if a steady current of 2A is maintained. Assuming the density of copper is 0.0088kg/cm³ and mass of copper liberated per columb is 3.3 × 10^-7kg/C

Correct Answer

C

Explanation

To calculate the time required to electroplate the substance, we can use the formula:

\[ \text{Time} = \frac{\text{Area} \times \text{Thickness}}{\text{Current} \times \text{Mass per Coulomb}} \]

First, we need to convert the area and thickness to meters and kilograms, respectively, for consistency in units.

Area = 300 cm² = 0.03 m² (since 1 m² = 10,000 cm²)
Thickness = 0.6 mm = 0.0006 m (since 1 m = 1000 mm)

Now, we can use the given values to calculate the time:

\[ \text{Time} = \frac{0.03 \, \text{m}^2 \times 0.0006 \, \text{m}}{2 \, \text{A} \times 3.3 \times 10^{-7} \, \text{kg/C}} \]

\[ \text{Time} = \frac{0.000018 \, \text{m}^3}{6.6 \times 10^{-7} \, \text{A} \cdot \text{kg/C}} \]

\[ \text{Time} = \frac{0.000018 \, \text{m}^3}{6.6 \times 10^{-7} \, \text{C} \cdot \text{kg/C}} \]

\[ \text{Time} = \frac{0.000018 \, \text{m}^3}{6.6 \times 10^{-7} \, \text{kg}} \]

\[ \text{Time} = 2.727 \times 10^4 \, \text{s} \]

So, the time required to electroplate the substance with a layer of copper 0.6 mm thick, given a steady current of 2A, is approximately 27,270 seconds.