A battery has e.m.f. 4 V and internal resistance r . When this battery is connected to an external resistance of 2 ohms , a current of 1 amp . flows in the circuit. How much current will flow if the terminals of the battery are connected directly

Options

A. 4 and 2
B. 2 and 4
C. 4 and 4
D. 2 and 2

Explanation

To solve the problem, we need to determine the internal resistance of the battery and then find the current that will flow when the battery terminals are connected directly.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- E.M.F. of the battery (E) = 4 V
- External resistance (R) = 2 ohms
- Current (I) = 1 A

2. **Apply Ohm's Law:**
- When the battery is connected to the external resistance, the total resistance in the circuit is the sum of the internal resistance (r) and the external resistance (R).
- According to Ohm's Law, the current (I) can be expressed as:
\[ I = \frac{E}{R + r} \]
- Substituting the known values:
\[ 1 = \frac{4}{2 + r} \]

3. **Solve for Internal Resistance (r):**
- Rearranging the equation gives:
\[ 2 + r = \frac{4}{1} \]
\[ 2 + r = 4 \]
\[ r = 4 - 2 \]
\[ r = 2 \, \text{ohms} \]

4. **Determine the Current when Connected Directly:**
- When the terminals of the battery are connected directly, the only resistance in the circuit is the internal resistance (r).
- The current (I') can be calculated using Ohm's Law again:
\[ I' = \frac{E}{r} \]
- Substituting the values:
\[ I' = \frac{4}{2} \]
\[ I' = 2 \, \text{A} \]

5. **Final Answer:**
- The current that will flow when the terminals of the battery are connected directly is **2 A**.