Question
Find the current through the $10\Omega$ resistor shown in figure.

Answer

In the circuit ADCBA,

$3\text{i}+6\text{i}_1-4.5=0$

In the circuit GEFCG,

$3\text{i}+6\text{i}_1=4.5$

$=10\text{i}-10\text{i}_1-6\text{i}_1=-3$

$\Rightarrow[10\text{i}+16\text{i}_1=-3]3\ ...(1)$

$[3\text{i}+6\text{i}_1=4.5]10\ ...(2)$

From (1) and (2)

$-108\text{i}_1=-54$

$\Rightarrow\text{i}_1=\frac{54}{108}=\frac{1}{2}=0.5$

$3\text{i}+6\times\frac{1}{2}-4.5=0$

$3\text{i}-1.5=0\Rightarrow\text{i}=0.5$

Current through $10\Omega$ resistor = 0A.

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