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 1000 cells connected in series, each with the same EMF (E) and internal resistance (r).

### Step-by-Step Solution:

**Step 1: Understand the Configuration**
- We have 1000 cells connected in series.
- Each cell has an EMF of E and an internal resistance of r.
- Since they are in series, the total EMF (V_total) and total internal resistance (R_total) can be calculated.

**Step 2: Calculate Total EMF and Total Internal Resistance**
- Total EMF (V_total) = Number of cells × EMF of each cell = 1000E
- Total internal resistance (R_total) = Number of cells × Internal resistance of each cell = 1000r

**Step 3: Apply Kirchhoff's Voltage Law**
- According to Kirchhoff's Voltage Law, the sum of the potential differences in a closed circuit is equal to the total EMF supplied.
- The equation for the circuit can be written as:
\[ V_{total} = I \times R_{total} \]
where I is the current flowing through the circuit.

**Step 4: Calculate the Current (I)**
- From the equation:
\[ 1000E = I \times 1000r \]
- We can simplify this to find the current:
\[ I = \frac{1000E}{1000r} = \frac{E}{r} \]

**Step 5: Calculate the Potential Drop across 399 Cells**
- The potential drop across 399 cells can be calculated using the formula:
\[ V_{399} = \text{Potential drop due to EMF} - \text{Potential drop due to internal resistance} \]
- The potential drop due to EMF from 399 cells:
\[ V_{emf} = 399E \]
- The potential drop due to internal resistance (for 399 cells):
\[ V_{internal} = I \times \text{Total internal resistance of 399 cells} = I \times 399r \]
- Substitute I from Step 4:
\[ V_{internal} = \left(\frac{E}{r}\right) \times 399r = 399E \]
- Therefore, the total potential drop across 399 cells is:
\[ V_{399} = 399E - 399E = 0 \]

### Final Answer:
The potential drop across 399 cells is **0 volts**.