A `50V` battery is connected across a 10 ohm resistor. The current is `4.5` amperes. The internal resistance of the battery is

Options

A. Zero
B. `0.5` ohm
C. `1.1` ohm
D. `5.0` ohm

Answer

To find the internal resistance of the battery, we can use the information provided in the question. Here’s a step-by-step solution:

### Step 1: Understand the given values
We have:
- EMF of the battery (E) = 50 V
- External resistance (R) = 10 Ω
- Current (I) = 4.5 A

### Step 2: Use Ohm's Law
According to Ohm's Law, the total voltage (EMF) in the circuit is equal to the sum of the voltage drops across the external resistor and the internal resistance of the battery. The formula can be expressed as:
\[ E = I(R + r) \]
Where:
- \( r \) is the internal resistance of the battery.

### Step 3: Rearranging the formula
We can rearrange the formula to solve for the internal resistance \( r \):
\[ r = \frac{E}{I} - R \]

### Step 4: Substitute the known values
Now, we can substitute the known values into the equation:
1. Calculate \( \frac{E}{I} \):
\[ \frac{E}{I} = \frac{50 \text{ V}}{4.5 \text{ A}} \]
\[ \frac{E}{I} = 11.11 \text{ Ω} \]

2. Now, substitute this value into the equation for \( r \):
\[ r = 11.11 \text{ Ω} - 10 \text{ Ω} \]
\[ r = 1.11 \text{ Ω} \]

### Step 5: Conclusion
The internal resistance of the battery is approximately:
\[ r \approx 1.1 \text{ Ω} \]

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