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Voltmeter

In the circui...

Question

In the circuit shown $E_{1} = 4.0 V, R_{1} = 2 Ω, E_{2} = 6.0 V, R_{2} = 4 Ω$ and $R_{3} = 2 Ω$ . The current $I_{1}$ is

A

1.6

A

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B

1.8

A

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C

1.25

A

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D

1.0

A

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Solution

The correct option is B $1.8$ A
Apply KVL in ABCD
$4 - 2 I_{1} - 4 I_{2} + 6 = 0 2 I_{1} + 4 I_{2} = 10 I_{1} + 2 I_{2} = 5 (1)$
$
Apply KVL in EDCF
$4 - 2 I_{1} + 2 (I_{2} - I_{1}) = 0 4 - 2 I_{1} + 2 I_{2} - 2 I_{1} = 0 4 I_{1} - 2 I_{2} = 4 (2)$
Add (1) and (2)
$5 I_{1} = 9 I_{1} = \frac{9 A}{5} = 1.8 A$

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