Question

The equivalent resistance between $A$ and $C$ of the given circuit, is

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

Answer 1

Answer: (B), (D)

From the given circuit, we find that $R _{BD}$ is ineffective as it is a balanced wheatstone bridge.
Since both the upper resistances are in a series combination, therefore their equivalent resistance $\left( R _{ U }\right)=2+2$ $=4 \Omega$.
Similarly both the lower resistances are in a series combination, therefore their equivalent resistance $\left( R _{ L }\right)=4+4=8 \Omega$.
Now we see that both the resistance $R _{U} \& R _{ L }$ are in a parallel combination.
Therefore equivalent resistance between
$A$ and $C =\frac{R_{U} \times R_{L}}{R_{U}+R_{L}}=\frac{4 \times 8}{4+8}=\frac{32}{12} \Omega=\frac{8}{3} \Omega$