First slide

KVL

Question

In the given circuit, the current I₁ is

Moderate

A

0.4 A
B

$- 0.4 A$
C

0.8 A
D

$- 0.8 A$

Solution

The circuit can be simplified as follows:
Applying KCL at junction A
$\Rightarrow I_{3} = I_{1} + I_{2} ..... (i)$
Applying Kirchhoff's voltage law for the loop ABCDA,
$\begin{array}{l} - 30 I_{1} - 40 I_{3} + 40 = 0 \\ \Rightarrow - 30 I_{1} - 40 (I_{1} + I_{2}) + 40 = 0 \\ \Rightarrow 7 I_{1} + 4 I_{2} = 4 . .... (ii) \end{array}$
Applying Kirchhoff's voltage law for the loop ADEFA,
$\begin{array}{l} - 40 I_{1} - 40 I_{3} + 80 + 40 = 0 \\ \Rightarrow - 40 I_{2} - 40 (I_{1} + I_{2}) = - 120 \\ \Rightarrow I_{1} + 2 I_{2} = 3 . .... (iii) \end{array}$
On solving equations (ii) and (iii), $I_{1} = - 0.44 A$

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