Question

Find the equivalent resistance between $A$ and $B$.

• A. $10\Omega$
• B. $5\Omega$
• C. $40\Omega$
• D. $30\Omega$

Answer 1

The correct option is B $5\Omega$

To solve this question, let us simplify the circuit by finding equivalent resistances of small sections.

To find $R_1,5\Omega$ resistors are in series. $R_1=5\Omega +5\Omega =10\Omega$

To find $R_2,10\Omega$ resistor and $R_1$ are in parallel.
$\frac{1}{R_2}=\frac{1}{10}+\frac{1}{R_1}$
$\frac{1}{R_2}=\frac{1}{10}+\frac{1}{10}=\frac{2}{10}$
$R_2=5\Omega$

To find $R_3$, $5\Omega$ resistor and $R_2$ are in series.​
$R_3=5\Omega +R_2$
$R_3=5\Omega +5\Omega =10\Omega$

To find $R$, $10\Omega$ resistor and $R_3$ are in parallel.​
$1/R=1/10+1/R_3$
$1/R=1/10+1/10=2/10$
$R=5\Omega$