(i) Calculate the equivalent resistances of the given electrical network between points A and B.
(ii) Also calculate the current through CD and ACB, if a 10 V d.c. source is connected between A and B, and the value of R is assummed as 2 Ω.

Solution

The equivalent circuit of the given circuit is

The above fig. is a balanced wheatstone bridge.
$∴$ Resistance across arm CD is 0.

i) Now,
Resistance across arm ACB , R₁= R+R = 2R
Resistance across arm ADB , R₂ = R+R = 2R

Effective resistance between AB is ,

$\frac{1}{R_{P}} = \frac{1}{2 R} + \frac{1}{2 R} = \frac{2}{2 R}$

$\Rightarrow$ R_p = R $Ω$

ii) The points C and D are at the same potential. Therefore, the current across arm CD is zero.

Resistance across arm ACB = 2R = 2(2) = 4 $Ω$

$∴$ Current flowing through ACB, I = $\frac{10}{4} = 2.5 A$

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Current Electricity

(i) Calculate the equivalent resistances of the given electrical network between points A and B.
(ii) Also calculate the current through CD and ACB, if a 10 V d.c. source is connected between A and B, and the value of R is assummed as 2 Ω.

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Current Electricity

(i) Calculate the equivalent resistances of the given electrical network between points A and B.(ii) Also calculate the current through CD and ACB, if a 10 V d.c. source is connected between A and B, and the value of R is assummed as 2 Ω.

Some More Questions From Current Electricity Chapter

Mock Test Series

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Entrance Exams Preparation

(i) Calculate the equivalent resistances of the given electrical network between points A and B.
(ii) Also calculate the current through CD and ACB, if a 10 V d.c. source is connected between A and B, and the value of R is assummed as 2 Ω.