A storage battery with emf `2.6 V` loaded with external resistance produces a current `1 A`. In this case, the potential difference between the terminals of the storage battery equals `2 V`. Find the thermal power generated in the battery and the net power supplied by the battery for external circuit.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the given values
- EMF of the battery, \( E = 2.6 \, \text{V} \)
- Current flowing through the circuit, \( I = 1 \, \text{A} \)
- Terminal voltage (potential difference across the battery), \( V = 2 \, \text{V} \)

### Step 2: Use the formula for terminal voltage
The terminal voltage \( V \) can be expressed in terms of EMF \( E \) and the internal resistance \( R \) of the battery:
\[ V = E - I \cdot r \]
Where \( r \) is the internal resistance of the battery.

### Step 3: Substitute the known values into the equation
Substituting the known values into the equation:
\[ 2 = 2.6 - 1 \cdot r \]

### Step 4: Solve for internal resistance \( r \)
Rearranging the equation:
\[ 1 \cdot r = 2.6 - 2 \]
\[ r = 0.6 \, \Omega \]

### Step 5: Calculate the thermal power generated in the battery
The thermal power \( P_{\text{thermal}} \) generated in the battery due to its internal resistance can be calculated using the formula:
\[ P_{\text{thermal}} = I^2 \cdot r \]
Substituting the values:
\[ P_{\text{thermal}} = 1^2 \cdot 0.6 = 0.6 \, \text{W} \]

### Step 6: Calculate the net power supplied by the battery to the external circuit
The total power supplied by the battery can be calculated using:
\[ P_{\text{total}} = E \cdot I \]
Substituting the values:
\[ P_{\text{total}} = 2.6 \cdot 1 = 2.6 \, \text{W} \]

### Step 7: Calculate the net power supplied to the external circuit
The net power \( P_{\text{net}} \) supplied to the external circuit is given by:
\[ P_{\text{net}} = P_{\text{total}} - P_{\text{thermal}} \]
Substituting the values:
\[ P_{\text{net}} = 2.6 - 0.6 = 2 \, \text{W} \]

### Final Answers
- Thermal power generated in the battery: \( 0.6 \, \text{W} \)
- Net power supplied by the battery for the external circuit: \( 2 \, \text{W} \)

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