What current is to be passed for `0.25` sec for deposition of certain weight of metal which is equal to its electrochemical equivalent ?

Options

A. 4A
B. 100A
C. 200A
D. 2A

Answer

To solve the problem of determining the current required for the deposition of a certain weight of metal equal to its electrochemical equivalent over a time period of 0.25 seconds, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**: The electrochemical equivalent (Z) is defined by the formula:
\[ Z = \frac{m}{I \cdot t} \]
where:
- \( Z \) is the electrochemical equivalent,
- \( m \) is the mass of the deposited metal,
- \( I \) is the current in amperes,
- \( t \) is the time in seconds.

2. **Given Information**:
- We know that the mass of the metal deposited \( m \) is equal to its electrochemical equivalent \( Z \).
- The time \( t \) is given as 0.25 seconds.

3. **Substituting the Given Values**: Since \( m = Z \), we can substitute \( m \) in the equation:
\[ Z = \frac{Z}{I \cdot t} \]

4. **Rearranging the Equation**: To isolate \( I \), we can rearrange the equation:
\[ I \cdot t = 1 \quad \text{(since \( Z \) cancels out)} \]
Thus, we have:
\[ I = \frac{1}{t} \]

5. **Calculating the Current**: Now, substituting \( t = 0.25 \) seconds into the equation:
\[ I = \frac{1}{0.25} \]
This simplifies to:
\[ I = 4 \, \text{A} \]

6. **Final Answer**: Therefore, the current that needs to be passed is:
\[ I = 4 \, \text{A} \]