Question

The potential difference between points $A$ and $B$ in the circuit shown in figure is 16 V. Then,

• A. the current through the $2\Omega$ resistance is 3.5 A
• B. the current through the $4\Omega$ resistance is 2.5 A
• C. the current through the $3\Omega$ resistance is 1.5 A
• D. the potential difference between the terminals of the 9 V battery is 7 V

Answer 1

Answer: (A), (C), (D)

The correct options are
A the current through the $3\Omega$ resistance is 1.5 A
C the current through the $2\Omega$ resistance is 3.5 A
D the potential difference between the terminals of the 9 V battery is 7 V

Applying Kirchhoff's law,
for loop CEFD, $9=2(I-I_1)-1I_1\Rightarrow 2I-3I_1=9...\left(1\right)$
For A to B via CD : $V_A-4I-9-1I_1+3-1I-3I=V_B$
or $V_A-V_B=6+8I+I_1$
or $16=6+8I+I_1\Rightarrow 8I+I_1=10...\left(2\right)$
$\left(1\right)\times 4-\left(2\right)\Rightarrow I_1=-2A$
so, $I=(9-6)/2=1.5A$
Current through $2\Omega =I-I_1=1.5+2=3.5A$
Current through $3\Omega =I=1.5A$
Current through $4\Omega =I=1.5A$
The potential difference between the terminals of the 9 V battery $=V_C-V_D=9+I_1=9-2=7V$