Question

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

• A. $30\Omega$
• B. $8\Omega$
• C. $10\Omega$
• D. $40\Omega$

Answer 1

Answer: (B)

The circuit can be shown as given below

The equivalent resistance between $A$ and $C$ .
$R_{DC}=\frac{15\times \left(15+15\right)}{15+\left(15+15\right)}$
$=\frac{15\times 30}{15+30}$
$=\frac{15\times 30}{45}=10\Omega$
Now, between $A$ and $B$ , the resistance of the upper part $ADCB,$
$R_1=15+10+15=40\Omega$
Between $A$ and $B$ , the resistance of the middle part $AOB$
$R_2=15+15=30\Omega$
Therefore, equivalent resistance between $A$ and $B$
$\frac{1}{R^{}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}$
$=\frac{1}{40}+\frac{1}{30}+\frac{1}{15}$
$=\frac{3+4+8}{120}$
$=\frac{15}{120}$
$\Rightarrow R^{}=\frac{120}{15}=8\Omega$