Question

A long resistor between point <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\text{A}$ and $\text{B}$ as shown in figure has resistance of $300\Omega$ and is tapped at one third points. Find the equivalent resistance between point $\text{A}$ and $\text{B}$ ?

• A. $16\Omega$
• B. $32\Omega$
• C. $48\Omega$
• D. Zero

Answer 1

The correct option is B $32\Omega$

In the given circuit the resistance $25\Omega$ is in parallel to $100\Omega$ resistance, thus equivalent resistance of these two resistances is given as,

$R_1=\frac{100\times 25}{100+25}=20\Omega$

Now the circuit is reduced as follows,


From above figure we can see that resistance $20\Omega$ and $100\Omega$ are in series and in parallel with $120\Omega$.

So the equivalent resistance is given as,

$R_2=\frac{120\times 120}{120+120}=60\Omega$

Now the circuit is further reduced as follows,


$100\Omega$ and $60\Omega$ resistance are in series which is in parallel with $40\Omega$ resistance. So the equivalent resistance between terminals <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\text{A}$ and $\text{B}$ is given as,

$R=\frac{160\times 40}{160+40}=32\Omega$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, option (b) is the correct answer.