The unknown resistance is approximately 0.44 Ω.
Solution:
Total (equivalent) resistance = 0.28 Ω
Resistance 1 = ?
Resistance 2 = 0.81 Ω
To find the unknown resistance.
Formula for determining equivalent resistance in a parallel circuit:
[tex]$\frac{1}{R_{e q}}=\frac{1}{R_{1}}+\frac{1}{R_{2}}[/tex]
Substitute the given values in the formula.
[tex]$\frac{1}{0.28}=\frac{1}{R_{1}}+\frac{1}{0.81}[/tex]
[tex]$3.571=\frac{1}{R_{1}}+1.235[/tex]
Subtract 1.235 on both sides of the equation, we get
[tex]$2.282=\frac{1}{R_{1}}[/tex]
Take reciprocal to find [tex]R_1[/tex].
[tex]$R_{1}=\frac{1}{2.282}[/tex]
[tex]$R_{1}=0.44[/tex]
[tex]R_1[/tex] = 0.44 Ω
The unknown resistance is approximately 0.44 Ω.
