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 $\varepsilon_1=12\, V$ and $\varepsilon_2=6\, V$.

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

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

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+36-3 V _0- V _0=0$
$ \Rightarrow 54=5 V _0 $
$ \frac{2\left(\frac{54}{5}- v ^{\prime}\right)}{1}+\frac{18- v ^{\prime}}{1}=0 $
$ \Rightarrow \frac{108}{5}+18=3 V ^{\prime}$
$ \Rightarrow v ^{\prime}=\frac{198}{5 \times 3}=\frac{66}{5} V$
$ I _{ R _1}=\frac{36}{5}=7.2 A $
$ I _{ R _2}=\frac{6}{5}=1.2 A$
$ I _{ R _3}=\frac{24}{5}=4.8 A $
$ I _{ R _5}=\frac{12}{5}=2.4 A $