Question

What is the equivalent resistance between $A$ and $B$ in the given circuit?

• A. $4\Omega$
• B. $2\Omega$
• C. $\frac{8}{3}\Omega$
• D. $\frac{3}{8}\Omega$

Answer 1

Answer: (C)

$\frac{8}{3}\Omega$

$R_1$ and $R_2$ are in series.
$\therefore R_{12}=R_1+R_2=4\Omega$

$R_{12}$ and $R_3$ are in parallel
$R_{123}=\frac{R_3\times R_{12}}{R_3+R_{12}}$
$=\frac{4\times 4}{4+4}=2\Omega$

$\therefore R_{123}$ and $R_4$ are in series
$\therefore R_{1234}$ and $R_5$ are in parallel
$R_{12345}=2\Omega$
$R_{12345}$ and $R_6$ are in series
$\therefore 2\Omega +2\Omega =4\Omega =R_{123456}$

Now, $R_{123456}$ and $R_7$ are in parallel
$\therefore R_{comb}=\frac{4\times 8}{4+8}=\frac{32}{12}=\frac{8}{3}\Omega$.