Five cells each of emf E and internal resistance r are connected 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 solve the problem of finding the equivalent EMF and internal resistance of a series combination of five cells, where one cell is connected incorrectly, we can follow these steps:

### Step 1: Understand the Configuration
We have 5 cells, each with an EMF of \( E \) and an internal resistance of \( r \). In a normal series connection, the EMFs would add up, and the internal resistances would also add up.

### Step 2: Identify the Incorrect Cell
Since one cell is connected incorrectly, it will oppose the EMF of the other cells. This means that instead of adding its EMF to the total, we will subtract it.

### Step 3: Calculate the Equivalent EMF
- In a normal series connection of 5 cells, the total EMF would be:
\[ E_{\text{total}} = E + E + E + E + E = 5E \]
- However, since one cell is connected in reverse, we subtract its EMF:
\[ E_{\text{equivalent}} = 5E - E = 4E \]

### Step 4: Calculate the Equivalent Internal Resistance
- The internal resistance of each cell is \( r \). Since all cells are in series, the total internal resistance is simply the sum of the internal resistances:
\[ R_{\text{equivalent}} = r + r + r + r + r = 5r \]

### Step 5: Final Result
Thus, the equivalent EMF and internal resistance of the combination are:
- Equivalent EMF: \( 4E \)
- Equivalent Internal Resistance: \( 5r \)

### Summary
The equivalent EMF of the combination is \( 4E \) and the equivalent internal resistance is \( 5r \).

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