Question

If the switches $S_1,S_2,and{S}_3$ in figure are arranged such that the current through the battery is minimum, find the voltage across points $A$ and $B$ (in mV).

Answer 1

Equivalent resistance of $1\Omega$ and $1\Omega$, $R^{\prime }=1\parallel 1=0.5\Omega$

Equivalent resistance between A and C, $R_{AC}=6+(9\parallel 9)=6+4.5=10.5\Omega$

Thus effective resistance of the whole circuit $R_{eq}=1+R_{AC}+R^{\prime }=1+10.5+0.5=12\Omega$

$\therefore$ Voltage across A and B $V_{AB}=\frac{R^{\prime }}{R_{eq}}V=\frac{0.5}{12}\times 24=1$ V