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)

The magnitude of current flowing through $R_1$ is $7.2\, A$.

Answer 2

(A) The magnitude of current flowing through R1 is 7.2 A.
(B) The magnitude of current flowing through R2 is 1.2 A.
(C) The magnitude of current flowing through R3 is 4.8 A.
(D) The magnitude of current flowing through R5 is 2.4 A.

From KCL
$i _ 1 ​ +i _ 2 ​ +i _3 ​ =0$
$⇒ \frac{18-V_0}{\frac{3}{2}} +\frac{12-V_0}{\frac{1}{2}}+\frac{0-V_0}{\frac{3}{2}}=0$

$⇒18−V _ 0 ​ +36−3V _0 ​ −V _ 0 ​ =0$
$⇒54=5V _ 0 ​$

$\frac{2(\frac{54}{5}-v')}{1}+\frac{18-v'}{1}=0$

$⇒v ′ =\frac{198}{ 5×3} ​ = \frac{ 66}{ ​ 5 } V$
$I _{ R 1} ​ ​ = \frac{36}{5} ​ =7.2A$
$I _{ R 2} = \frac{6}{5} ​ =1.2A$
$I _{ R 3} ​ ​ = \frac{24}{5} ​ =4.8A$
$I _ {R 5} ​ ​ = \frac{12}{5} ​ =2.4A$