Question

A wheatstone bridge ABCD is arranged as follows AB=1 ohm ;BC= 2ohm CD=3ohm; DA=4ohm; . A resistance of 5ohm is connected between B and D. A 4volt battery of internal resistance 1ohm is connected between A and C .Calculate 1. the magnitude and direction of current in 5ohm resistor and 2. the resistance between A and C​

Answer 1

Answer:

NOW, cramer's rule say that: l1=lx/l, l2=ly/l, l3=lz/l. That is....

l1= 550÷230=55/23A

l2= 200÷230=20/23A

l3= 50÷230=5/23A

Voltage across BD,

V=l3×5=5/23×5=10/23= 0.435 ..... Answer...

give me brainlist answer plz......

Answer 2

Answer:

(i) The current in the 5 ohm resistor is 0.087A and the direction is from B to D.

(ii) The resistance between A and C​ is $2.065 ohm$.

Explanation:

Given a Wheatstone bridge ABCD.

The Wheatstone Bridge is a simple circuit used for measuring an unknown resistance by comparing its value with that of known resistance.

Applying KVL in loop ABDA

$-I_1-5I_3+4I_2=0$

$I_1+5I_3-4I_2=0$       ...........(1)

Applying KVL in loop BCDB

$-2(I_1-I_3)+3(I_2+I_3)+5I_3=0$

$-2I_1+2I_3+3I_2+3I_3+5I_3=0$

$-2I_1+10I_3+3I_2=0$

$2I_1-10I_3-3I_2=0$       ........(2)

Applying KVL in FABCEF

$-I_1-2(I_1-I_3)-1(I_1+I_2)+4=0$

$-I_1-2I_1+2I_3-I_1-I_2+4=0$

$-4I_1+2I_3-I_2=4$

$4I_1-2I_3+I_2=4$      ...........(3)

Equation (1)×2-(2)

⇒$20I_3-5I_2=0$  ...........(4)

Equation (1) X 4-(3)

$22I_3-17I_2=-4$   ........(5)

Equation (5)×4-(4)×17

⇒ $230I_3=20$

$I_3=\frac{20}{230}=0.087A$

(i) The current in the 5 ohm resistor is 0.087A and the direction is from B to D.

$I_3=0.087A$, substituting in equation (4) gives $I_2=0.348A$

Substituting I_3 and I_2 in equation (2) we get $I_1=0.957A$

Current supplied by battery, $I=I_1+I_2$

$I=0.957+0.348$

$I=1.305 A$

Potential difference or voltage between A and C = EMF of battery - Drop in battery.

$V=4-1.305=2.695V$

Resistance between A and C = Voltage across AC Battery current

$R=\frac{2.695 }{1.305}$

$R=2.065 ohm$

(ii) Therefore, the resistance between A and C​ is $2.065 ohm$.

To know more about Wheatstone bridge go to the following link.

https://brainly.in/question/84419

To know more about current go to the following link.

https://brainly.in/question/1151879

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