Question

The ratio of resistances between A and B before and after the switch S is closed:

• A. $9:8$
• B. $7:8$
• C. $2:3$
• D. $1:2$

Answer 1

The correct option is A $9:8$

Using Kirchhoff's law:

Before closing switch S:

$R_{eff}=\frac{9\times 9}{2\times 9}=\frac{9}{2}$
After closing the switch S, the circuit can be drawn as shown.

$V=I{R}_{eff}$

$V=6\times \frac{I}{3}+\frac{2I}{3}\times 3$

$V=4I$

$R_{eff}=4$

$Ratio=\frac{\frac{9}{2}}{4}=\frac{9}{8}$