5 cells, each of emf 0.2V and internal resistance `1 Omega` are connected to an external circuit of resistance of `10 Omega`. Find the current through external circuit-

Options

A. `1/2.5 A`
B. `1/10 A`
C. `1/15 A`
D. `1/2 A`

Explanation

To find the current through the external circuit with the given cells, we can follow these steps:

### Step 1: Determine the total EMF of the cells
Since the cells are connected in series, the total EMF (E_total) is the sum of the individual EMFs of the cells.

Given:
- Each cell has an EMF of 0.2 V.
- There are 5 cells.

\[ E_{\text{total}} = 5 \times 0.2 \, \text{V} = 1.0 \, \text{V} \]

### Step 2: Determine the total internal resistance
The internal resistance of each cell is given as 1 Ω. Since they are connected in series, the total internal resistance (R_internal) is the sum of the individual internal resistances.

Given:
- Internal resistance of each cell = 1 Ω
- Number of cells = 5

\[ R_{\text{internal}} = 5 \times 1 \, \Omega = 5 \, \Omega \]

### Step 3: Calculate the total resistance in the circuit
The total resistance in the circuit (R_total) is the sum of the total internal resistance and the external resistance (R_external).

Given:
- External resistance (R_external) = 10 Ω

\[ R_{\text{total}} = R_{\text{internal}} + R_{\text{external}} = 5 \, \Omega + 10 \, \Omega = 15 \, \Omega \]

### Step 4: Use Ohm's Law to find the current
Ohm's Law states that the current (I) in a circuit is equal to the total voltage (E_total) divided by the total resistance (R_total).

\[ I = \frac{E_{\text{total}}}{R_{\text{total}}} = \frac{1.0 \, \text{V}}{15 \, \Omega} = \frac{1}{15} \, \text{A} \]

### Final Answer
The current through the external circuit is \( \frac{1}{15} \, \text{A} \).

---