Question

Using three wires of resistance $1ohm,2ohm$ and $3ohm$, then no. of different values of resistances that possible are:

• A. $6$
• B. $4$
• C. $10$
• D. $8$

Answer 1

The correct option is D $8$

$R_1=1\Omega ,R_2=2\Omega ,quad{R}_3=3\Omega$

Case-$1$, when all are in series, $R_{eq}=6\Omega$

Case-$2$, when all are in series, $R_{eq}=6/11\Omega$

Case-$3,R_1$ and $R_2$ in series and their resultant is parallel with $R_3=3/2\Omega$

Case-$4,R_1$ and $R_2$ in parallel and their resultant is series with $R_3=11/3\Omega$

Case-$5,R_1$ and $R_2$ in series and their resultant is parallel with $R_2=R_{eq}=4/3\Omega$

Case-$6,R_1$ and $R_2$ in series and their resultant is parallel with $R_2=R_{eq}=11/4\Omega$

Case-$7,R_2$ and $R_3$ in series and their resultant is parallel with $R_1=R_{eq}=5/6\Omega$

Case-$8,R_2$ and $R_3$ in parallel and their resultant is series with $R_2=R_{eq}=11/5\Omega$

$\therefore$ There are $8$ possible ways, we can also find out by using formula $2^n$ where $n:$ no of resistance.