Five cells each of emf E and internal resistance r are connecte in series. Due to oversight one cell is connected wrongly . The equivalent emf and internal resistance of the combination is

Options

A. `3E, 3r`
B. 5E , 3r
C. 3E, 5r
D. 5E,5r

Answer

To find the equivalent emf and internal resistance of the combination of five cells connected in series, with one cell connected in reverse, we can follow these steps:

### Step 1: Understand the Configuration
We have five cells, each with an emf (E) and an internal resistance (r). Four cells are connected in the correct orientation, while one cell is connected in reverse.

### Step 2: Calculate the Equivalent EMF
The equivalent emf (E_eq) of cells in series is the sum of their individual emfs. For the four cells connected correctly, their contribution to the emf is:
- E1 = E
- E2 = E
- E3 = E
- E4 = E

The fifth cell, which is connected in reverse, contributes negatively:
- E5 = -E

Thus, the equivalent emf can be calculated as:
\[ E_{eq} = E1 + E2 + E3 + E4 + E5 = E + E + E + E - E \]
\[ E_{eq} = 4E - E = 3E \]

### Step 3: Calculate the Equivalent Internal Resistance
The internal resistances of cells in series simply add up. Since all cells have the same internal resistance (r), the equivalent internal resistance (R_eq) will be:
\[ R_{eq} = r1 + r2 + r3 + r4 + r5 = r + r + r + r + r \]
\[ R_{eq} = 5r \]

### Final Result
Therefore, the equivalent emf and internal resistance of the combination of the cells is:
- Equivalent EMF = 3E
- Equivalent Internal Resistance = 5r

### Summary
The equivalent emf of the combination is 3E and the equivalent internal resistance is 5r.

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