In the circuit shown, the reading of the ammeter (ideal) is the same with both switches open as with both closed find the value of resistance $R$ in $ohm$ . ................ $\Omega$
Diffcult
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$I=\frac{1.5}{450} \mathrm{\,A}$
$R_{a b}=\frac{R \times 100}{100+R}$
$\quad \mathrm{V}_{\mathrm{ab}}=\frac{1.5}{300+\mathrm{R}_{\mathrm{ab}}} \times \mathrm{R}_{\mathrm{ab}}$
$\mathrm{I}=\frac{\mathrm{V}_{\mathrm{ab}}}{100}=\frac{1.5}{300+\frac{\mathrm{R} \times 100}{100+\mathrm{R}}} \times \frac{100 \mathrm{R}}{100+\mathrm{R}} \times \frac{1}{100}$
$ = \frac{{1.5{\rm{R}}}}{{300 \times \left( {100 + {\rm{R}}} \right) + 100{\rm{R}}}}$
$\therefore = \frac{{1.5{\rm{R}}}}{{300 \times 100 + 300{\rm{R}} + 100 \times 100}} = \frac{{1.5{\rm{R}}}}{{100 + {\rm{R}}}}$
$\Rightarrow 50 \mathrm{R}=300 \times 100$
$\Rightarrow \mathrm{R}=600\, \Omega$
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