First slide

combination of resistance

Question

Three resistances P, Q, R each of $2 Ω$ and an unknown resistance S form the four arms of a Wheatstone's bridge circuit. When a resistance of $6 Ω$ is connected in parallel to s the bridge gets balanced. what is the value of S?

Moderate

A

$2 Ω$
B

$3 Ω$
C

$6 Ω$
D

$1 Ω$

Solution

The bridge formed with given resistances is a balanced Wheatstone's bridge
The situation can be depicted as shown in the figure.
As resistances S and $6 Ω$ are in parallel, their effective resistance is $\frac{6 S}{6 + S} Ω .$
For balancing condition, $\frac{P}{Q} = \frac{R}{(\frac{6 S}{6 + S})}$
$\begin{array}{l} or \frac{2}{2} = \frac{2 (6 + S)}{6 S} \\ or 3 S = 6 + S \Rightarrow S = 3 Ω \end{array}$

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