What is the potential difference across 100 Ω resistor in the circuit given below?

What is the potential difference across 100 Ω resistor in the circuit given below?

Solution:
Let,
$R_1$ = 100 $\mathrm{\Omega }$
$R_2$ = 50 $\mathrm{\Omega }$
$R_3$ = 500 $\mathrm{\Omega }$
V = 12 V $\mathrm{\Omega }$

Since $R_1$ and $R_2$ are parallel, the equivalent resistance is, $$\begin{array}{rl}\frac{1}{R_{12}}& =\frac{1}{R_1}+\frac{1}{R_2}\\ \frac{1}{R_{12}}& =\frac{3}{100}\\ \therefore R_{12}& =\frac{100}{3}\end{array}$$ Total resistance in the circuit is then, $$\begin{array}{rl}R& =R_{12}+R_3\\ & =\frac{100}{3}+500\\ & =\frac{1600}{3}\\ \therefore R& =\frac{1600}{3}\mathrm{\Omega }\end{array}$$ Now, $$\begin{array}{rl}V& =IR\\ 12& =I\times \frac{1600}{3}\\ I& =\frac{36}{1600}A\end{array}$$ Then, voltage across 100 $\mathrm{\Omega }$ resistor is, $$\begin{array}{rl}& =I\times R_{12}\\ & =\frac{36}{1600}\times \frac{100}{3}\\ & =0.75V\end{array}$$
Hence, the potential difference across 100 $\mathrm{\Omega }$ resistor is 0.75 V.