Ten cells each of emf `1 V` and internal resistance `1Omega` are connected inseries. In this arrangement, polarity of two cells is reversed and the system is connected to an external resistance of `2Omega`. Find the current in the circuit.

Explanation

To solve the problem step by step, we will analyze the circuit with the given parameters.

### Step 1: Identify the parameters
We have:
- Number of cells, \( n = 10 \)
- EMF of each cell, \( E = 1 \, \text{V} \)
- Internal resistance of each cell, \( r = 1 \, \Omega \)
- External resistance, \( R = 2 \, \Omega \)
- Two cells have their polarity reversed.

### Step 2: Calculate the total EMF
When two cells have their polarity reversed, they effectively subtract their EMF from the total. Therefore, the total EMF can be calculated as follows:

\[ \text{Total EMF} = (n - 2) \cdot E = (10 - 2) \cdot 1 = 8 \, \text{V} \]

So, the effective EMF after reversing the polarity of two cells is:

\[ E_{\text{equiv}} = 8 \, \text{V} - 2 \, \text{V} = 6 \, \text{V} \]

### Step 3: Calculate the total internal resistance
Since all cells are in series, the total internal resistance can be calculated as:

\[ R_{\text{internal}} = n \cdot r = 10 \cdot 1 = 10 \, \Omega \]

### Step 4: Calculate the total resistance in the circuit
The total resistance in the circuit is the sum of the internal resistance and the external resistance:

\[ R_{\text{total}} = R_{\text{internal}} + R = 10 \, \Omega + 2 \, \Omega = 12 \, \Omega \]

### Step 5: Calculate the current in the circuit
Using Ohm's law, the current \( I \) in the circuit can be calculated using the formula:

\[ I = \frac{E_{\text{equiv}}}{R_{\text{total}}} = \frac{6 \, \text{V}}{12 \, \Omega} = \frac{1}{2} \, \text{A} \]

### Final Answer
The current in the circuit is \( I = 0.5 \, \text{A} \).

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