Question

Equivalent resistance across A and B in the given circuit if $r=10\Omega$ $R=20\Omega$ is

• A. $7\Omega$
• B. $14\Omega$
• C. $35\Omega$
• D. $20/3\Omega$

Answer 1

Answer: (B)

$14\Omega$

Let the potential at point A be E, at the junction be x and E-x as shown and that at B be zero.

So using the junction rule at point of potential $x$ we have

$\frac{E-2x}{r}-\frac{x}{r}=\frac{x-E}{R}$

or

$\frac{E-3x}{r}=\frac{x-E}{R}$

or

$x=\frac{E(R+r)}{r+3R}$

Now we write

$\frac{E-x}{R}+\frac{x}{r}=\frac{E}{R_{eq}}$

Solving this equation we get

$R_{eq}=\frac{r(r+3R)}{3r+R}$

using the values we get,

$R_{eq}=10\left(\frac{3\left(20\right)+10}{3\left(10\right)+20}\right)$

$R_{eq}=10\left(\frac{70}{50}\right)$

$R_{eq}=14\Omega$