Question

In the circuit shown the reading of ammeter (ideal) is the same with both switches open as with both closed. Find the value of resistance R is $\Omega$

• A. $700\Omega$
• B. $300\Omega$
• C. $70\Omega$
• D. $100\Omega$

Answer 1

The correct option is A $700\Omega$

$\begin{array}{c}Whentheswitchesareopenthentheresis\tan ceofthewholecircuitis,\\ R_{eq}=100+300+50=450\Omega \\ Nowwhentheswitchesareclosedthentheresis\tan ceofthecircuitis,\\ R_{eq}=\frac{100R}{100+R}+300+50=\frac{100R}{100+R}+350\\ Nowasthecurrentissamewhentheswitchisopenorclosedthen,\\ \frac{1.5}{450}=\left[\frac{1.5}{\frac{100R}{100+R}+300}\right]\times \frac{R}{\left(100+R\right)}=\frac{1.5\left(10++R\right)}{100R+35000+300R}\times \frac{R}{\left(100+R\right)}\\ \Rightarrow 450R+35000=400R\\ R=\frac{35000}{50}=700\Omega \end{array}$