Question

Find out the equivalent resistance....​

Answer 1

Question :-

Find the equivalent resistance between X and Y.

Answer :-

Let's name the resistors as $\tt R_1,~ R_2, ~R_3....R_8$.

• Refer the attachment 1.

The resistors $\tt R_2, ~R_3$ are in parallel arrangement.

$\implies \tt \frac{1}{R_p} = \frac{1}{R_2} + \frac{1}{R_3}$

$\implies \tt \frac{1}{R_p} = \frac{1}{3} + \frac{1}{5}$

$\implies \tt \frac{1}{R_p} = \frac{5+3}{15}$

$\implies \tt \frac{1}{R_p} = \frac{8}{15}$

$\implies \tt R_p= \frac{15}{8} \Omega$

Also, $\tt R_6,~R_7,~R_8$ are in parallel arrangement.

$\implies \tt \frac{1}{R_p} = \frac{1}{R_6} + \frac{1}{R_7} + \frac{1}{R_8}$

$\implies \tt \frac{1}{R_p} = \frac{1}{1} + \frac{1}{2} + \frac{1}{2}$

$\implies \tt \frac{1}{R_p} = \frac{2+1+1}{2}$

$\implies \tt \frac{1}{R_p} = \frac{4}{2}$

$\implies \tt R_p = \frac{1}{2} \Omega$

Now, the setup looks like this :

• Refer the attachment 2.

Let them be named again as $\tt R_1,~R_2....R_5$.

The resistors $\tt R_2,~R_4$ are in series arrangement.

$\implies \tt R_s=R_2+R_4$

$\implies \tt R_s= \frac{15}{8} +1$

$\implies \tt R_s= \frac{15+8}{8}$

$\implies \tt \frac{23}{8} \Omega$

Also, $\tt R_3,~R_5$ are in series arrangement.

$\implies \tt R_s=R_3+R_5$

$\implies \tt R_s=2+ \frac{1}{2}$

$\implies \tt R_s= \frac{4+1}{2}$

$\implies \tt R_s= \frac{5}{2} \Omega$

Now, the setup looks again like this :

• Refer the attachment 3.

Here, $\tt R_2,~R_3$ are in parallel arrangement.

$\implies \tt \frac{1}{R_p} = \frac{1}{ \frac{23}{8} } + \frac{1}{ \frac{5}{2} }$

$\implies \tt \frac{1}{R_p} = \frac{8}{23} + \frac{2}{5}$

$\implies \tt \frac{1}{R_p} = \frac{40+46}{115}$

$\implies \tt \frac{1}{R_p} = \frac{86}{115}$

$\implies \tt R_p= \frac{115}{86} \Omega$

And the final setup looks like this :

• Refer the attachment 4.

Here, $\tt R_1,~R_2$ are in series arrangement.

$\implies \tt R_s=R_1+R_2$

$\implies \tt R_s =2 + \frac{115}{86}$

$\implies \tt R_s= \frac{172 +115}{86}$

$\implies \tt R_s= \frac{287}{86}$

$\implies \tt R_s=3.33 \Omega$

$\underline {\boxed {\mathfrak{\therefore~Equivalent~resistance=3.33 \Omega}}}$