To find the equivalent resistance in a series circuit, you simply add up the resistance values of each resistor. This is because in a series circuit, the total resistance is the sum of all the individual resistances.
Given the resistances:
- [tex]\(R_1 = 40.0 \Omega\)[/tex]
- [tex]\(R_2 = 25.4 \Omega\)[/tex]
- [tex]\(R_3 = 70.8 \Omega\)[/tex]
We use the formula for equivalent resistance in a series circuit:
[tex]\[ R_{\text{eq}} = R_1 + R_2 + R_3 \][/tex]
Substituting the given values:
[tex]\[ R_{\text{eq}} = 40.0 \Omega + 25.4 \Omega + 70.8 \Omega \][/tex]
Adding these together:
[tex]\[ R_{\text{eq}} = 136.2 \Omega \][/tex]
Therefore, the equivalent resistance [tex]\( R_{\text{eq}} \)[/tex] is [tex]\( 136.2 \Omega \)[/tex].
