To solve the problem of finding the total resistance when three resistances are connected in series, we can follow these steps:
1. Identify the given resistances:
- [tex]\( R_1 = 2 \Omega \)[/tex]
- [tex]\( R_2 = 4 \Omega \)[/tex]
- [tex]\( R_3 = 5 \Omega \)[/tex]
2. Understand the concept of series connection:
- When resistances are connected in series, their total resistance can be found by simply summing up their individual resistances.
3. Formula for total resistance in series:
[tex]\[ R_{\text{total}} = R_1 + R_2 + R_3 \][/tex]
4. Apply the given values to the formula:
[tex]\[ R_{\text{total}} = 2 \Omega + 4 \Omega + 5 \Omega \][/tex]
5. Calculate the total resistance:
[tex]\[ R_{\text{total}} = 11 \Omega \][/tex]
So, the total resistance when resistances of [tex]\(2 \Omega\)[/tex], [tex]\(4 \Omega\)[/tex], and [tex]\(5 \Omega\)[/tex] are connected in series is [tex]\(11 \Omega\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{11 \Omega} \][/tex]
Hence, the correct option is:
[tex]\[ \text{b. } 11 \Omega \][/tex]
