A battery of emf 10 V and internal resistance `3Omega`is connected to a resistor. The current in the circuit is 0.5 A . The terminal voltage of the battery when the circuit is closed is

Options

A. 10 V
B. 0V
C. 1.5 V
D. 8.5 V

Explanation

To find the terminal voltage of the battery when the circuit is closed, we can follow these steps:

### Step 1: Identify the given values
- Electromotive force (emf) of the battery, \( E = 10 \, \text{V} \)
- Internal resistance of the battery, \( r = 3 \, \Omega \)
- Current in the circuit, \( I = 0.5 \, \text{A} \)

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

### Step 3: Substitute the values into the formula
Substituting the known values into the formula:
\[ V = 10 \, \text{V} - (0.5 \, \text{A} \cdot 3 \, \Omega) \]

### Step 4: Calculate the product of current and internal resistance
Calculating \( I \cdot r \):
\[ I \cdot r = 0.5 \, \text{A} \cdot 3 \, \Omega = 1.5 \, \text{V} \]

### Step 5: Calculate the terminal voltage
Now substitute back into the equation for \( V \):
\[ V = 10 \, \text{V} - 1.5 \, \text{V} = 8.5 \, \text{V} \]

### Final Answer
The terminal voltage of the battery when the circuit is closed is:
\[ \boxed{8.5 \, \text{V}} \]

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