Question

Find the electric current drawn from the battery of emf 12 V.

• A. 1 A
• B. 4 A
• C. 2 A
• D. 3 A

Answer 1

The correct option is C 2 A

Let current $I_3$ is drawn from the battery of 12 V.
This is divided into 2 streams of current $I_1$ and $I_2$.
With help of kirchhoff's law on junction E
$I_3=I_1+I_2$

Using the loop law,
For the loop EADFE, starting from a 12 V battery and going anti-clockwise.
Loop EADFA
Applying KVL , from 12V battery
$12-5-2I_1-3(I_1+I_2)=0$
$7-2I_1-3I_1-3I_2=0$
$7-5I_1-3I_2=0$
$5I_1+3I_2=7$ ……..(1)

Using the loop law,
For the loop EBCFE, starting from a 12 V battery and going clockwise.

Loop EBCFE
Applying KVL , from 12V battery
$12-4I_2-3(I_1+I_2)=0$
$12-4I_2-3I_1-3I_2=0$
$12-3I_1-7I_2=0$
$3I_1+7I_2=12$ …….(2)

Solving eq (1) and eq(2)
$3(5I_1+3I_2=7)=>15I_1+9I_2=21$
$5(3I_1+7I_2=12)=>15I_1+35I_2=60$
$-26\times I_2=-39$
$I_2=1.5A$ putting this in eq (1)
$5I_1+3\times 1.5=7$
$5I_1=2.5$
$I_1=0.5A$

$I_3=I_1+I_2=0.5A+1.5A=2A$