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Question

Determine the current in 2 $Ω$ resistor

1 A
1.5 A
0.9 A
0.6 A

A

1.5 A

B

1 A

C

0.9 A

D

0.6 A

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Solution

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A fully charged capacitor no current draws from cell. So, no current flow in the capacitor branch and corresponding circuit is shown in figure.
Total resistance of the circuit is $R_{t} = 2.8 + 2 | | 3 = 2.8 + \frac{2 \times 3}{2 + 3} = 2.8 + 1.2 = 4 Ω$
Current in the circuit is $I = \frac{6}{4} = 1.5 A$
If $I_{1}$ and $I_{2}$ are the current through $2 Ω$ and $3 Ω$ respectively, then $I = I_{1} + I_{2} . . . (1)$
As $2 Ω$ and $3 Ω$ are in parallel so $V_{2 Ω} = V_{3 Ω}$ or $2 I_{1} = 3 I_{2} \Rightarrow I_{2} = (2 / 3) I_{1}$
now, (1) becomes, $1.5 = I_{1} + (2 / 3) I_{1} = \frac{5 I_{1}}{3}$
or $I_{1} = \frac{1.5 \times 3}{5} = 0.9 A$

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