In the following network, the current flowing | vedclass

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

Question

(B) Let the nodes be $A, B, C, D$ as shown in the figure. The total current entering the network at node $A$ is $I = 2.1 	ext{ A}$.Let $I_1$ be the c

Vedclass · Accepted Answer

$0.9$

Vedclass · Answer

(B) Let the nodes be $A, B, C, D$ as shown in the figure. The total current entering the network at node $A$ is $I = 2.1 	ext{ A}$.Let $I_1$ be the current flowing through the $15 	ext{ } \Omega$ resistor (branch $AB$) and $I_2$ be the current flowing through the $20 	ext{ } \Omega$ resistor (branch $AD$).By Kirchhoff's Current Law at node $A$, $I_1 + I_2 = 2.1 	ext{ A}$.Using Kirchhoff's Voltage Law for the loops:For loop $ABDA$: $15I_1 + 6I_G - 20I_2 = 0$, where $I_G$ is the current through the galvanometer ($6 	ext{ } \Omega$ resistance).For loop $BCDB$: $3(I_1 - I_G) - 4(I_2 + I_G) - 6I_G = 0 \implies 3I_1 - 4I_2 - 13I_G = 0$.Solving these equations for $I_1$ with the condition that the bridge is not balanced, we find the potential at $B$ and $D$ relative to $A$. Alternatively, using nodal analysis: Let $V_A = V$, $V_C = 0$. Let $V_B$ and $V_D$ be the potentials at $B$ and $D$.$(V - V_B)/15 = (V_B - V_C)/3 + (V_B - V_D)/6$$(V - V_D)/20 = (V_D - V_C)/4 + (V_D - V_B)/6$Solving this system for $V_B$ and $V_D$ with $I = (V - V_B)/15 + (V - V_D)/20 = 2.1$, we get $I_1 = 0.9 	ext{ A}$.

In the following network, the current flowing through $15 \text{ } \Omega$ resistance is (in $\text{ A}$)

Similar Questions

What is the equivalent resistance between $X$ and $Y$ in the given circuit?

As shown in the circuit diagram,find the value of $I = \text{ . . . . . . }$. (in $\text{ A}$)

In the following circuit,find the current through the path $ACB$ if each resistance $R = 4 \ \Omega$ and the battery voltage is $16 \ V$. (in $A$)

State and explain Kirchhoff's first law (Junction law) and Kirchhoff's second law (Loop rule).

In the following network,$I_{1} = -0.4 \text{ A}$,$I_{4} = 1 \text{ A}$ and $I_{5} = 0.4 \text{ A}$. The values of $I_{2}$,$I_{3}$ and $I_{6}$ respectively are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module