1. **Problem Statement:** We need to find how many 2-character passwords are possible using the English alphabet with case sensitivity. 2. **Understanding the problem:** The English alphabet has 26 letters. Since the passwords are case sensitive, each letter can be either uppercase or lowercase, making 52 possible characters for each position. 3. **Formula:** The total number of possible passwords of length $n$ with $k$ possible characters for each position is given by: $$\text{Total passwords} = k^n$$ 4. **Applying the formula:** Here, $k = 52$ (26 uppercase + 26 lowercase) and $n = 2$. $$\text{Total passwords} = 52^2$$ 5. **Calculating:** $$52^2 = 52 \times 52 = 2704$$ 6. **Answer:** There are 2704 possible 2-character case sensitive passwords.