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Mixed Combination of Cells

Find the curr...

Question

Find the current through the $10 Ω$ resistor shown in figure:

A

0.5 A

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B

1 A

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C

2 A

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D

5 A

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Solution

The correct option is A $0.5 A$
Given circuit
Applying KVL in loop 1
$- 4.5 + 3 i_{1} + 6 (i_{1} - i_{2}) = 0$
$\Rightarrow 3 i_{1} + 6 i_{1} - 6 i_{2} = 4.5 \Rightarrow 9 i_{1} - 6 i_{2} = 4.5$ ___(1)
KVL in loop 2
$- 3 v + 10 i_{2} + 6 (i_{2} - i_{1}) = 0$
$\Rightarrow - 6 i_{1} = 16 i_{2} = 3 v$ __(2)
solving (1) & (2)
$9 i_{1} - 6 i_{2} = 4.5 \Rightarrow 18 i_{1} - 12 i_{2} = 9$
$- 6 i_{1} + 16 i_{2} = 3 \Rightarrow - 18 i_{1} + 48 i_{2} = 9$
$36 i_{2} = 18 = i_{2} = 18 / 36 = 1 / 2 = 0.5 A$
$- 6 i_{1} + 16 (1 / 2) = 3 v$
$- 6 i_{1} = 3 - 8$
$i = 5 / 6 = 0.833$
$∴$ The current flowing through $10 Ω$ resister is $0.5 A$

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