First slide

combination of resistance

Question

In the given circuit, what will be the equivalent resistance between the points A and B ?

Moderate

A

$10 / 3 Ω$
B

$20 / 3 Ω$
C

$2 Ω$
D

$5 Ω$

Solution

This is a case of balanced Wheatstone bridge because
$\frac{P}{Q} = \frac{R}{S} or \frac{2}{3} = \frac{4}{6}$
Therefore, no current will flow through 10 $Ω$ resistance .now, the equivalent resistance can be calculated by using fig
Here, $R_{ACB} = (2 + 3) = 5 Ω$
and $R_{ADB} = (4 + 6) = 10 Ω$
Now, $R_{ACB} and R_{ABB}$ are in parallel
$∴ \frac{1}{R_{resultant}} = \frac{1}{5} + \frac{1}{10} = \frac{2 + 1}{10} = \frac{3}{10}$
or $R_{T} = (10 / 3) Ω$

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