Q135 / 170 · Manipal (MET) 2019 · Physics
Find the equivalent resistance across $A B$


- Correct answerA$1 \Omega$
- B$2 \Omega$
- C$3 \Omega$
- D$4 \Omega$
Solution
$R_1$ and $R_2$ are in parallel order, so their equivalent resistance
$R^{\prime}=\frac{2 \times 2}{2+2}=1 \Omega$
Similarly, equivalent resistance of $R_3$ and $R_4$ $R^{\prime \prime}=1 \Omega$
$R^{\prime}$ and $R^{\prime \prime}$ are in series order, so their equivalent resistance $\begin{aligned} R^{\prime \prime \prime} & =R^{\prime}+R^{\prime \prime} \\ & =1+1=2 \Omega \end{aligned}$ $R^{\prime \prime \prime}$ and $R_5$ are in parallel. So, $\quad R_{A B}=\frac{2 \times 2}{2+2}=1 \Omega$
Similarly, equivalent resistance of $R_3$ and $R_4$ $R^{\prime \prime}=1 \Omega$

$R^{\prime}$ and $R^{\prime \prime}$ are in series order, so their equivalent resistance $\begin{aligned} R^{\prime \prime \prime} & =R^{\prime}+R^{\prime \prime} \\ & =1+1=2 \Omega \end{aligned}$ $R^{\prime \prime \prime}$ and $R_5$ are in parallel. So, $\quad R_{A B}=\frac{2 \times 2}{2+2}=1 \Omega$
Hence, the correct answer is option: 'A'.