What is the value of i_3 in the given circuit | vedclass

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

Question

(D) Let the potential at the top junction be $V$ and the bottom junction be $0 \, V$. Applying Kirchhoff's Current Law $(KCL)$ at the top junction:$\f

Vedclass · Accepted Answer

$-5/6 \, A$

Vedclass · Answer

(D) Let the potential at the top junction be $V$ and the bottom junction be $0 \, V$. Applying Kirchhoff's Current Law $(KCL)$ at the top junction:$\frac{V - 8}{28} + \frac{V - 12}{54} + \frac{V - 6}{0} = 0$ is not applicable directly due to the branch with only a battery. Instead,use nodal analysis.Let the potential at the top node be $V_x$ and the bottom node be $0 \, V$.The current $i_3$ flows downwards through the $6 \, V$ battery.Using the node voltage method:$\frac{V_x - 8}{28} + \frac{V_x - 12}{54} + \frac{V_x - 6}{0}$ is incorrect. Let's use loop analysis.In loop $1$ (left): $28 i_1 + 6 + 8 = 0 \Rightarrow 28 i_1 = -14 \Rightarrow i_1 = -0.5 \, A$.In loop $2$ (right): $54 i_2 + 6 + 12 = 0 \Rightarrow 54 i_2 = -18 \Rightarrow i_2 = -1/3 \, A$.At the central node,by $KCL$: $i_3 = i_1 + i_2 = -0.5 - 1/3 = -3/6 - 2/6 = -5/6 \, A$.

What is the value of $i_3$ in the given circuit?

Similar Questions

In a balanced Wheatstone bridge,the current in the galvanometer is zero. It remains zero when:

The Wheatstone bridge shown in the diagram is balanced. If $P_3$ is the power dissipated by $R_3$ and $P_1$ is the power dissipated by $R_1$,then the ratio $\frac{P_3}{P_1}$ is

In the circuit shown,what is the potential difference $V_{PQ}$?

Consider the following circuit shown below. All the resistors are identical. The ratio of $I / I^{\prime}$ is

What are the uses of a Wheatstone bridge?

Vedclass Test Series

Exam Paper Generator

Online Exam Module