First slide

KVL

Question

In the circuit shown below $E_{1} = 4 .0 V, R_{1} = 2 Ω, E_{2} = 6 .0 V, R_{2} = 4 Ω and R_{3} = 2 Ω .$ The current i₁ is

Moderate

A

1.6 A
B

1.8 A
C

1.25 A
D

1.0 A

Solution

Applying Kirchhoff's law for the loops (l) and (2) as shown in figure.
For loop (1),
$- 2 i_{1} - 2 (i_{1} - i_{2}) + 4 = 0 \Rightarrow 2 i_{1} - i_{2} = 2 . .. (i)$
For loop (2),
$- 2 (i_{1} - i_{2}) + 4 i_{2} - 6 = 0 \Rightarrow - i_{1} + 3 i_{2} = 3 . .. (ii)$
On solving equations (i) and (ii), i₁ = 1.8 A

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