Question

The figure shows a circuit having eight resistances of $1\Omega$ each, labelled $R_1$ to $R_8$, and two ideal batteries with voltages ${\epsilon }_1=12V$ and ${\epsilon }_2=6V$.

Which of the following statement(s) is(are) correct?

• A. The magnitude of current flowing through $R_1$ is $7.2A$.
• B. The magnitude of current flowing through $R_2$ is $1.2A$.
• C. The magnitude of current flowing through $R_3$ is $4.8A$.
• D. The magnitude of current flowing through $R_5$ is $2.4A$.

Answer 1

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

From KCL
$i_1+i_2+i_3=0$
$\Rightarrow \frac{18-V_0}{3/2}+\frac{12-V_0}{1/2}+\frac{0-V_0}{3/2}=0$
$\Rightarrow 18-V_0+36-3V_0-V_0=0$
$\Rightarrow 54=5V_0$
$\frac{2\left(\frac{54}{5}-v^{\prime }\right)}{1}+\frac{18-v^{\prime }}{1}=0$
$\Rightarrow \frac{108}{5}+18=3V^{\prime }$
$\Rightarrow v^{\prime }=\frac{198}{5\times 3}=\frac{66}{5}V$
$I_{R_1}=\frac{36}{5}=7.2A$
$I_{R_2}=\frac{6}{5}=1.2A$
$I_{R_3}=\frac{24}{5}=4.8A$
$I_{R_5}=\frac{12}{5}=2.4A$