The equivalent resistance between the points $A$ and $B$ will be (each resistance is $15 Ω$ )

Question

The equivalent resistance between the points A and B will be (each resistance is 15 Ω )

TestHub · Accepted Answer

The circuit can be shown as given below

The equivalent resistance between $A$ and $C$ .

$R_{D C} = \frac{15 \times (15 + 15)}{15 + (15 + 15)}$

$= \frac{15 \times 30}{15 + 30}$

$= \frac{15 \times 30}{45} = 10 Ω$

Now, between $A$ and $B$ , the resistance of the upper part $ADCB,$

$R_{1} = 15 + 10 + 15 = 40 Ω$

Between $A$ and $B$ , the resistance of the middle part $AOB$

$R_{2} = 15 + 15 = 30 Ω$

Therefore, equivalent resistance between $A$ and $B$

$\frac{1}{R^{}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}}$

$= \frac{1}{40} + \frac{1}{30} + \frac{1}{15}$

$= \frac{3 + 4 + 8}{120}$

$= \frac{15}{120}$

$\Rightarrow R^{} = \frac{120}{15} = 8 Ω$

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