The terminal potential difference for a cell is 8.5 V when current is 2A and 9 V when current is 1.5A. What is the internal resistance of cell ?

Options

A. `4Omega`
B. `2Omega`
C. `3Omega`
D. `1Omega`

Explanation

To find the internal resistance of the cell, we can use the information provided in the question. We have two conditions with different currents and terminal potential differences. Let's denote:

- \( V \) = terminal potential difference (voltage)
- \( I \) = current
- \( r \) = internal resistance of the cell
- \( E \) = electromotive force (emf) of the cell

From the problem, we have the following two conditions:

1. When \( I = 2 \, \text{A} \), \( V = 8.5 \, \text{V} \)
2. When \( I = 1.5 \, \text{A} \), \( V = 9 \, \text{V} \)

We can use the formula relating these quantities:

\[ V = E - I \cdot r \]

From the first condition:

\[ 8.5 = E - 2r \quad \text{(1)} \]

From the second condition:

\[ 9 = E - 1.5r \quad \text{(2)} \]

Now, we can solve these two equations simultaneously.

### Step 1: Rearranging the equations
From equation (1):

\[ E = 8.5 + 2r \quad \text{(3)} \]

From equation (2):

\[ E = 9 + 1.5r \quad \text{(4)} \]

### Step 2: Setting the equations equal
Since both equations (3) and (4) equal \( E \), we can set them equal to each other:

\[ 8.5 + 2r = 9 + 1.5r \]

### Step 3: Solving for \( r \)
Now, we can solve for \( r \):

\[ 8.5 + 2r - 1.5r = 9 \]
\[ 8.5 + 0.5r = 9 \]
\[ 0.5r = 9 - 8.5 \]
\[ 0.5r = 0.5 \]
\[ r = \frac{0.5}{0.5} = 1 \, \Omega \]

### Conclusion
The internal resistance of the cell is \( r = 1 \, \Omega \).