Question

The equivalent resistance between point $A$ and $B$ in the line adjoining circuit diagram will be:

• A. $\frac{13}{17}\Omega$
• B. $\frac{1}{4}\Omega$
• C. $\frac{3}{5}\Omega$
• D. $4\Omega$

Answer 1

The correct option is A $\frac{13}{17}\Omega$

In this question anti symmetry is present.

$\therefore$ Current is $1\Omega$ and $3\Omega$ will be same.

Apply KVL in $\left(1\right)$

$-i-5(2i-I)+3(I-i)=0$

$-i-10i+5I+3I-3i=0$

$=8I=14i$

$I=\frac{7i}{4}$

Apply KVL in $\left(2\right)$

$5(2i-I)-3(I-i)+i=$

$10i-5I-3I+3i+i=0$

$I=\frac{7i}{4}$

Apply KVL in $\left(3\right)$

$-3(I-i)-i+V=0$

$V=i+3(I-i)$

$=i+3I-3i$

$3I-2i$

$3I-2\times \frac{4\pi }{7}$

$=3I-\frac{8}{7}I$

$V=\frac{13I}{7}$

$V=I_{req}$

$\therefore R_{eq}=\frac{13}{17}\Omega$