Question

If twelve resistors each of 5 ohm are connected between points
A and B, then
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Answer 1

Answer:

correct answer is c... dear

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Answer 2

Answer:

The equivalent resistance between A and B is $R_{AB} =\frac{3R}{2} \Omega$

Explanation:

Given the resistance of each resistor, $R=5 \Omega$  

In each branch 2 resistors are connected in parallel, therefore the equivalent resistance of each branch is

                                        $\frac{1}{R_{eq} } =\frac{1}{R_{1} }+\frac{1}{R_{2} }$

                                $\implies \frac{1}{R_{eq} } =\frac{1}{5 }+\frac{1}{5 }\implies {R_{eq} }=\frac{5}{2} \Omega$

The center branch now have two branches with two resistors in series.

The equivalent resistance of resistors in series is

                                       ${R_{eq} ={R_{1} }+}{R_{2} }$

                                $\implies{R_{eq} } =\frac{5}{2 }+\frac{5}{2 }\implies {R_{eq} }=5 \Omega$

Now it makes again a branch of 2 resistors of 5Ω connected in parallel. Therefore the equivalent resistance is $\frac{5}{2} \Omega$

Now the three resistors are in series as shown in the figure.

Therefore the equivalent resistance is

                             $\implies{R_{eq} } =\frac{5}{2 }+\frac{5}{2 }+\frac{5}{2 }$

                             $\implies {R_{eq} }=\frac{3\times5}{2} \Omega=\frac{3R}{2} \Omega$

Hence, the equivalent resistance between A and B is $R_{AB} =\frac{3R}{2} \Omega$