In the above question, if the balancing length for a cell of emf `E` is `60 cm`, the value of `E` will be

Options

A. `3 mV`
B. `5 mV`
C. `6 mV`
D. `2000 mV`

Explanation

To find the value of the EMF \( E \) given the balancing length and the potential gradient, follow these steps:

### Step 1: Understand the relationship between EMF, potential gradient, and balancing length.
The potential gradient \( k \) is defined as the potential difference per unit length. It can be expressed mathematically as:
\[ k = \frac{E}{L} \]
where:
- \( E \) is the EMF of the cell,
- \( L \) is the balancing length.

### Step 2: Rearrange the formula to solve for EMF \( E \).
From the equation above, we can rearrange it to find \( E \):
\[ E = k \times L \]

### Step 3: Substitute the known values into the equation.
From the previous question, we know:
- The potential gradient \( k = 5 \, \text{mV/m} = 5 \times 10^{-3} \, \text{V/m} \)
- The balancing length \( L = 60 \, \text{cm} = 60 \times 10^{-2} \, \text{m} = 0.6 \, \text{m} \)

Now substituting these values into the equation:
\[ E = (5 \times 10^{-3} \, \text{V/m}) \times (0.6 \, \text{m}) \]

### Step 4: Perform the multiplication.
Calculating the above:
\[ E = 5 \times 0.6 \times 10^{-3} = 3 \times 10^{-3} \, \text{V} \]

### Step 5: Convert the result to millivolts.
Since \( 1 \, \text{V} = 1000 \, \text{mV} \):
\[ E = 3 \, \text{mV} \]

### Final Answer:
The value of the EMF \( E \) is \( 3 \, \text{mV} \).

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