Question

Consider the star network shown in figure. The resistance between terminals A and B with terminals C open is $6\Omega$, between terminals B and C with terminal A open is $11\Omega$, and between terminals C and A with terminal B open is $9\Omega$. Then

• A. $R_A=4\Omega ,R_B=2\Omega ,R_C=5\Omega$
• B. $R_A=2\Omega ,R_B=4\Omega ,R_C=7\Omega$
• C. $R_A=3\Omega ,R_B=3\Omega ,R_C=4\Omega$
• D. $R_A=5\Omega ,R_B=1\Omega ,R_C=10\Omega$

Answer 1

The correct option is B $R_A=2\Omega ,R_B=4\Omega ,R_C=7\Omega$

When C is open,
$R_{AB}=R_A+R_B=6\Omega$

When B is open,
$R_{AC}=R_A+R_C=9\Omega$

When A is open,
$R_{BC}=R_B+R_C=11\Omega$

On solving above equations

$R_A=2\Omega ,R_B=4\Omega and{R}_c=7\Omega$