In the circuit shown below, the ammeter reading is zero. Then the value of the resistance $R$ is

In the circuit shown below, the ammeter reading is zero. Then the value of the resistance $R$ is
  1. $50 \Omega$
  2. $100 \Omega$
  3. $200 \Omega$
  4. $400 \Omega$

Solution

Given, circuit
In loop (1) $12-500 i_1-R i_1=0$
In loop (2) $12-500 i_1-2=0 \Rightarrow 10=500 i_1$
From Eqs. (i) and (ii) $\begin{gathered} 12 \times \frac{1}{i_1}=(500+R) \\ \Rightarrow \quad 12 \times 50=500+R \Rightarrow R=100 \Omega \end{gathered}$

Asked in: AP EAMCET 2011

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