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

The Correct Option is A, B, C, D

(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
\(i _ 1 ​  +i _ 2 ​  +i  _3 ​  =0\)
\(⇒  \frac{18-V_0}{\frac{3}{2}} +\frac{12-V_0}{\frac{1}{2}}+\frac{0-V_0}{\frac{3}{2}}=0\)

\(⇒18−V _ 0 ​  +36−3V  _0 ​  −V _ 0 ​  =0\)
\(⇒54=5V _ 0 ​  \)

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

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