Question

In the given circuit diagram, battery has internal resistance of $6\Omega$. For what value of $r$, external circuit will consume maximum power?

• A. $5\Omega$
• B. $6\Omega$
• C. $9\Omega$
• D. $3\Omega$

Answer 1

The correct option is C $9\Omega$

We know that for maximum power consumption by external circuit, external resistance should be equal to internal resistance of the battery.

Lets calculate the external resistance. Given external circuit is symmetrical about the line $123$ and it is perpendicular to $AB$.


So, due to the perpendicular axis symmetry, point $1$, $2$ and $3$ are equipotential. So resistors between them can be removed since current will not flow through them.

Now, the resistors between $A-1$ and $1-B$ are in series. Their equivalent resistance will be $r+r=2r$. Similarly resistors $A-2$, $2-B$ and $A-3$, $3-B$ have equivalent resistance $2r$.

Now all three are in parallel combination. Equivalent resistance of external circuit, $R_{ex}=\frac{2r}{3}$

Now, from maximum power transfer theorem, $R_{ex}=6$

$\Rightarrow \frac{2r}{3}=6$

$\therefore r=9\Omega$