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(B) $1$. Analyze the circuit diagram to identify series and parallel combinations.$2$. Observe that the resistors $3 \ \Omega$ and $1 \ \Omega$ are in

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$8$

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(B) $1$. Analyze the circuit diagram to identify series and parallel combinations.$2$. Observe that the resistors $3 \ \Omega$ and $1 \ \Omega$ are in series,giving a total of $4 \ \Omega$. This combination is in parallel with the $2 \ \Omega$ resistor,but further inspection shows that the path through the $1.8 \ \Omega$ and $2.2 \ \Omega$ resistors is short-circuited by the central wire.$3$. By simplifying the circuit step-by-step as shown in the provided solution image,the effective resistance reduces to a simple series combination of $2 \ \Omega$,$1 \ \Omega$,and $5 \ \Omega$.$4$. The equivalent resistance $R_{AB} = 2 \ \Omega + 1 \ \Omega + 5 \ \Omega = 8 \ \Omega$.

In the given circuit,the equivalent resistance between $A$ and $B$ is ....... $\Omega$.

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