A car battery of emf 12V and internal resistance `0.05 omega` receives a current of 60 A from an external source, then the terminal potential difference of the battery is

Options

A. 12 V
B. 9 V
C. 15 V
D. 20 V

Explanation

To find the terminal potential difference of the battery, we can follow these steps:

### Step 1: Identify the given values
- Electromotive force (emf) of the battery, \( E = 12 \, \text{V} \)
- Internal resistance of the battery, \( r = 0.05 \, \Omega \)
- Current flowing from the external source, \( I = 60 \, \text{A} \)

### Step 2: Use the formula for terminal potential difference
The terminal potential difference \( V \) of a battery can be calculated using the formula:
\[ V = E - I \cdot r \]
where:
- \( V \) is the terminal potential difference,
- \( E \) is the emf of the battery,
- \( I \) is the current,
- \( r \) is the internal resistance.

### Step 3: Substitute the values into the formula
Now, we will substitute the given values into the formula:
\[ V = 12 \, \text{V} - (60 \, \text{A} \cdot 0.05 \, \Omega) \]

### Step 4: Calculate the product of current and internal resistance
Calculate \( I \cdot r \):
\[ I \cdot r = 60 \, \text{A} \cdot 0.05 \, \Omega = 3 \, \text{V} \]

### Step 5: Calculate the terminal potential difference
Now substitute back into the equation for \( V \):
\[ V = 12 \, \text{V} - 3 \, \text{V} = 9 \, \text{V} \]

### Final Answer
The terminal potential difference of the battery is \( V = 9 \, \text{V} \).

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