Let's go through the calculations step-by-step based on the formula given for [tex]\( R_T \)[/tex]:
[tex]\[ R_T = \frac{R_n}{2} \][/tex]
1. For [tex]\( R_n = 100 \Omega \)[/tex]:
[tex]\[ R_T = \frac{100}{2} = 50.0 \Omega \][/tex]
2. For [tex]\( R_n = 25 \Omega \)[/tex]:
[tex]\[ R_T = \frac{25}{2} = 12.5 \Omega \][/tex]
3. For [tex]\( R_n = 200 \Omega \)[/tex]:
[tex]\[ R_T = \frac{200}{2} = 100.0 \Omega \][/tex]
4. For [tex]\( R_n = 400 \Omega \)[/tex]:
[tex]\[ R_T = \frac{400}{2} = 200.0 \Omega \][/tex]
5. For [tex]\( R_n = 50 \Omega \)[/tex]:
[tex]\[ R_T = \frac{50}{2} = 25.0 \Omega \][/tex]
Thus, the values of [tex]\( R_T \)[/tex] for the given [tex]\( R_n \)[/tex] values are:
- When [tex]\( R_n = 100 \Omega \)[/tex], [tex]\( R_T = 50.0 \Omega \)[/tex]
- When [tex]\( R_n = 25 \Omega \)[/tex], [tex]\( R_T = 12.5 \Omega \)[/tex]
- When [tex]\( R_n = 200 \Omega \)[/tex], [tex]\( R_T = 100.0 \Omega \)[/tex]
- When [tex]\( R_n = 400 \Omega \)[/tex], [tex]\( R_T = 200.0 \Omega \)[/tex]
- When [tex]\( R_n = 50 \Omega \)[/tex], [tex]\( R_T = 25.0 \Omega \)[/tex]
The final rounded results are:
[tex]\[ [50.0, 12.5, 100.0, 200.0, 25.0] \][/tex]
