A 50V battery is connected across a 10 ohm resistor. The current is 4.5A is flowing through the resistor then the internal resistance of the battery is

Options

A. zero
B. `0.5Omega`
C. `1.1Omega`
D. `5Omega`

Answer

To find the internal resistance of the battery, we can use the following steps:

### Step 1: Understand the Circuit
We have a battery with an electromotive force (emf) of 50V connected to a resistor of 10 ohms. The current flowing through the circuit is 4.5A.

### Step 2: Write the Formula for Current
The current (I) flowing through the circuit can be expressed using Ohm's law, which states:
\[ I = \frac{E}{R_{total}} \]
where:
- \( E \) is the emf of the battery,
- \( R_{total} \) is the total resistance in the circuit, which includes both the external resistance (R) and the internal resistance (r) of the battery.

### Step 3: Express Total Resistance
The total resistance in the circuit can be expressed as:
\[ R_{total} = R + r \]
where:
- \( R \) is the external resistance (10 ohms),
- \( r \) is the internal resistance of the battery (which we need to find).

### Step 4: Substitute Values into the Formula
From the current formula, we can substitute the total resistance:
\[ I = \frac{E}{R + r} \]
Rearranging gives us:
\[ R + r = \frac{E}{I} \]

### Step 5: Plug in the Known Values
Now, substituting the known values:
- \( E = 50V \)
- \( I = 4.5A \)

So,
\[ R + r = \frac{50V}{4.5A} \]
Calculating this gives:
\[ R + r = \frac{50}{4.5} \approx 11.11 \, \text{ohms} \]

### Step 6: Calculate Internal Resistance
Now we can find the internal resistance \( r \) by rearranging the equation:
\[ r = R + r - R \]
Substituting \( R = 10 \, \text{ohms} \):
\[ r = 11.11 - 10 \]
\[ r \approx 1.11 \, \text{ohms} \]

### Final Answer
The internal resistance of the battery is approximately **1.11 ohms**.

---