Question

plz answer the above question .109.
✔ITS A CHALLENGING QUESTION...✔▶❕❕​

Answer 1

Answer:

(a) 2r/3

Explanation:

you can merge point q and m into m as there is no resistance between them. now this figure becomes 2r and 2r resistances in parallel between p and m which solves into r.

next, this combination was in series with r between l and p. solving the earlier solved r with this r gives 2r. now this entire chain is in parallel with the r resistance shown in figure between l and q, which now means between l and m since we merged the two points at the beginning of this solution. so, 2r and r in parallel gives us the solution 2r/3.

Answer 2

Answer:

$\large\bold\red{(a)\frac{2r}{3}}$

Explanation:

In the given Circuit,

If we observe it carefully,

we come across the conclusion that,

current gets divided at the point P

Now,

we know that,

The circuit where current gets divided is in parallel circuit.

Also,

Resistance across PLQ is in series,

We know that,

Equivalent resistance in series is given by,

$\bold{R_{eq}=R_{1}+R_{2}}$

Therefore,

here we have,

$R_{eq}= r+r = 2r$

Now,

we have ,

3 resistance of each (2r) Ω in parallel connection.

Also,

we know that,

Equivalent Resistance in parallel is given by,

$\bold{\frac{1}{R_{eq}}=\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}}}$

Therefore,

we have,

$=>\frac{1}{2r}=\frac{1}{2r}+\frac{1}{2r}+\frac{1}{2r}$

$=>\frac{1}{R_{eq}}=\frac{3}{2r}$

$=>\bold{R_{eq}=\frac{2r}{3}}$

Hence,

Correct option is $\bold{(a)\frac{2r}{3}}$