What is the current in A flowing through BD i | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $i_1$ be the current in the left loop and $i_2$ be the current flowing through the resistor in branch $BD$.Applying Kirchhoff's Voltage Law $(

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(A) Let $i_1$ be the current in the left loop and $i_2$ be the current flowing through the resistor in branch $BD$.Applying Kirchhoff's Voltage Law $(KVL)$ to the left loop (starting from $D$ to $A$ to $B$ to $D$):$15 - 6i_1 - 3i_2 = 0 \implies 6i_1 + 3i_2 = 15 \implies 2i_1 + i_2 = 5$ ... $(i)$Applying $KVL$ to the right loop (starting from $D$ to $B$ to $C$ to $D$):$-3(i_1 - i_2) - 30 + 3i_2 = 0$ (Note: The current through $BC$ is $i_1 - i_2$ based on the junction rule at $B$)$-3i_1 + 3i_2 + 3i_2 = 30 \implies -3i_1 + 6i_2 = 30 \implies -i_1 + 2i_2 = 10$ ... $(ii)$Multiplying equation $(i)$ by $1$ and equation $(ii)$ by $2$:$2i_1 + i_2 = 5$$-2i_1 + 4i_2 = 20$Adding the two equations:$5i_2 = 25 \implies i_2 = 5 \, A$.Thus,the current flowing through $BD$ is $5 \, A$.

What is the current in $A$ flowing through $BD$ in the given circuit?

Similar Questions

When the switch $S$, in the circuit shown, is closed, then the value of current $i$ will be ................. $A$.

Kirchhoff's first law,$i.e.$,$\Sigma i = 0$ at a junction,is based on the law of conservation of:

In the arrangement of resistors shown in the diagram,the potential difference between $B$ and $D$ will be zero when the unknown resistance $X$ is ............... $\Omega$.

The figure shows a network of four resistances and three batteries. The current through the branch $CF$ is ............... $A$.

In the shown circuit,what is the potential difference across $A$ and $B$ (in $V$)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module