Thousand cells of same emf E and same internal resistance r are connected is series in same order without an external resistance . The potential drop across 399 cells is found to be .

Options

A. Zero
B. 399E
C. 601E
D. 1000E

Answer

To solve the problem step by step, we will analyze the situation involving the cells connected in series.

### Step 1: Understand the Configuration
We have 1000 cells connected in series. Each cell has the same electromotive force (emf) \( E \) and the same internal resistance \( r \).

**Hint:** Remember that when cells are connected in series, the total emf and total internal resistance can be calculated by summing the individual emfs and resistances.

### Step 2: Calculate Total emf and Total Resistance
The total emf \( E_{total} \) of the series connection is:
\[ E_{total} = 1000E \]
The total internal resistance \( R_{total} \) of the series connection is:
\[ R_{total} = 1000r \]

**Hint:** The total emf is the sum of the individual emfs, and the total resistance is the sum of the individual resistances.

### Step 3: Determine the Current in the Circuit
Using Ohm's Law, the current \( I \) flowing through the circuit can be calculated as:
\[ I = \frac{E_{total}}{R_{total}} = \frac{1000E}{1000r} = \frac{E}{r} \]

**Hint:** The current can be found by dividing the total voltage by the total resistance.

### Step 4: Calculate the Potential Drop Across One Cell
The potential drop \( V \) across one cell can be calculated using the formula:
\[ V = E - I \cdot r \]
Substituting the value of \( I \):
\[ V = E - \left(\frac{E}{r}\right) \cdot r = E - E = 0 \]

**Hint:** The potential drop across a cell can be found by subtracting the voltage drop due to the internal resistance from the emf of the cell.

### Step 5: Determine the Potential Drop Across 399 Cells
Since the potential drop across each cell is 0, the potential drop across 399 cells is:
\[ V_{399} = 399 \cdot 0 = 0 \]

**Hint:** If the potential drop across one cell is zero, it will also be zero for any number of cells in series.

### Conclusion
Thus, the potential drop across 399 cells is \( 0 \).

**Final Answer:** The potential drop across 399 cells is \( 0 \).