For the given following circuit diagram, the dissipated of electrical power 150 W , then find the value of resistance \(R=\)_______.

C
dissipated power
\(\begin{aligned} P & =\frac{ V ^2}{ R _{e q}} \\ \therefore 150 & =\frac{(15)^2}{ R _{e q}} \\ \therefore \quad R _{e q} & =\frac{225}{150}\end{aligned}\)
Total resistance of the circuit \(R _{e q}=1.5 \Omega\)
\(\begin{aligned} \frac{1}{ R _{e q}} & =\frac{1}{ R _1}+\frac{1}{ R _2} \\ \frac{1}{1.5} & =\frac{1}{ R }+\frac{1}{2} \\ \therefore \quad & \frac{1}{ R }=\frac{1}{1.5}-\frac{1}{2} \\ \therefore \quad & \frac{1}{ R }=\frac{2-1.5}{2 \times 1.5} \\ \therefore \quad & \frac{1}{ R }=\frac{0.5}{3} \\ \therefore \quad & \frac{1}{ R }=\frac{1}{6} \\ \therefore \quad & R =6 \Omega\end{aligned}\)