Problem

Find the values of i1 and i2 in Figure P2.35.

Find the values of i1 and i2 in Figure P2.35.

Step-by-Step Solution

Solution 1

Given circuit is

The above circuit can be drawn as

In the above circuit, 6 and 12 are in parallel therefore

$$ \begin{aligned} R_{e q} &=\frac{6 \times 12}{6+12} \\ R_{e q} &=4 \Omega \end{aligned} $$

Now the circuit reduces to

Circuit (iii)

In the above circuit 4 and 4 are in series, now the circuit reduces to

$$ \begin{aligned} &i_{1}=\frac{20}{8} \\ &i_{1}=2.5 \mathrm{~A} \end{aligned} $$

From the circuit (iii)

$$ \begin{aligned} &v_{1}=4 \times i_{1} \\ &v_{1}=4 \times 2.5 \\ &v_{1}=10 \mathrm{~V} \\ &v_{2}=4 \times i_{1} \\ &v_{2}=4 \times 2.5 \\ &v_{2}=10 \mathrm{~V} \end{aligned} $$

From the circuit (ii)

$$ \begin{aligned} &i_{3}=\frac{v_{1}}{6} \\ &i_{3}=\frac{10}{6} \\ &i_{3}=1.6667 \\ &i_{4}=\frac{v_{2}}{12} \\ &i_{4}=\frac{10}{12} \\ &i_{4}=0.8333 \end{aligned} $$

Applying KCL at node a

$$ \begin{aligned} &-i_{3}+i_{2}+i_{4}=0 \\ &-1.6667+i_{2}+0.8333=0 \\ &i_{2}=0.8334 \mathrm{~A} \end{aligned} $$

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