Question

calculate the time in minutes required to electroplate an article of 300cm^2 with a layer of copper = 0.06 in thick if a constant. current of 24 is maintained. Assume that the density of a copper is 8.8gc^-1 and that 1 coulomb liberates 0.0033g of copper.

Answer 1

Answer on Question #73184, Physics / Electric Circuits

Question. Calculate the time in minutes required to electroplate an article of $S = 300 \, \text{cm}^2$ with a layer of copper $h = 0.06 \, \text{mm}$ in thick if a constant current of $I = 24 \, \text{A}$ is maintained. Assume that the density of a copper is $\rho = 8.8 \, \text{g/cm}^3$ and that 1 coulomb liberates $\Delta m = 0.0033 \, \text{g}$ of copper.

Given. $S = 300 \, \text{cm}^2$; $h = 0.06 \, \text{mm}$; $I = 24 \, \text{A}$; $\rho = 8.8 \, \text{g/cm}^3$; $\Delta m = 0.0033 \, \text{g/C}$.

Find. $t - ?$

Solution.

So, the volume of copper

$$V = S \cdot h.$$ $$\rho = \frac{m}{V} \rightarrow m = \rho \cdot V = \rho \cdot S \cdot h.$$

For a constant current

$$I = \frac{q}{t} \rightarrow q = I \cdot t.$$

Hence

$$\frac{m}{\Delta m} = q \rightarrow \frac{m}{\Delta m} = I \cdot t \rightarrow \frac{\rho \cdot S \cdot h}{\Delta m} = I \cdot t \rightarrow$$ $$\rightarrow t = \frac{\rho \cdot S \cdot h}{\Delta m \cdot I} = \frac{8800 \cdot 300 \cdot 10^{-4} \cdot 0.06 \cdot 10^{-3}}{0.0033 \cdot 10^{-3} \cdot 24} = 200 \, \text{s}$$

Answer. $t = 200 \, \text{s}$

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