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If [tex]$R_1=40.0 \Omega$[/tex], [tex]$R_2=25.4 \Omega$[/tex], and [tex]$R_3=70.8 \Omega$[/tex], what is the equivalent resistance?

[tex]$R_{\text{eq}} = [?] \Omega$[/tex]


Sagot :

To find the equivalent resistance [tex]\( R_{\text{eq}} \)[/tex] when the resistors [tex]\( R_1 \)[/tex], [tex]\( R_2 \)[/tex], and [tex]\( R_3 \)[/tex] are connected in series, we need to sum their 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]

In a series circuit, the equivalent resistance [tex]\( R_{\text{eq}} \)[/tex] is the sum of all the resistances in the series. Therefore, we calculate:

[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]

Performing the addition:

[tex]\[ R_{\text{eq}} = 40.0 + 25.4 + 70.8 \][/tex]

[tex]\[ R_{\text{eq}} = 136.2 \, \Omega \][/tex]

Therefore, the equivalent resistance is:

[tex]\[ R_{\text{eq}} = 136.2 \, \Omega \][/tex]