Question 583: Current Electricity

Question

In a wheatstone's bridge, three resistances $$\mathrm{P}, \mathrm{Q}$$ and $$\mathrm{R}$$ are connected in the three arms and the fourth arm is formed by two resistances $$S_1$$ and $$S_2$$ connected in parallel. The condition for the bridge to be balanced is

Accepted Answer

In a Wheatstone's bridge, we have four arms with resistances. For the given problem, three resistances $$\mathrm{P}$$, $$\mathrm{Q}$$, and $$\mathrm{R}$$ are connected in three arms, and the fourth arm is formed by the parallel combination of two resistances $$S_1$$ and $$S_2$$.
The condition for the Wheatstone's bridge to be balanced is that the ratio of the resistances in one pair of opposite arms is equal to the ratio of the resistances in the other pair of opposite arms.
Let's first find the equivalent resistance of the parallel combination of $$S_1$$ and $$S_2$$. The equivalent resistance $$S_{	ext{eq}}$$ for resistances in parallel is given by:
$$ \frac{1}{S_{	ext{eq}}} = \frac{1}{S_1} + \frac{1}{S_2} $$
Solving for $$S_{	ext{eq}}$$, we get:
$$ S_{	ext{eq}} = \frac{S_1 S_2}{S_1 + S_2} $$
Now, applying the condition for the Wheatstone's bridge to be balanced:
$$ \frac{P}{Q} = \frac{R}{S_{	ext{eq}}} $$
Substituting the equivalent resistance $$S_{	ext{eq}}$$, we get:
$$ \frac{P}{Q} = \frac{R}{\frac{S_1 S_2}{S_1 + S_2}} = \frac{R (S_1 + S_2)}{S_1 S_2} $$
So, the condition for the bridge to be balanced is:
$$ \frac{P}{Q} = \frac{R (S_1 + S_2)}{S_1 S_2} $$
Therefore, the correct option is:
Option C

Answer

$$\frac{P}{Q}=\frac{2 R}{S_1+S_2}$$

Answer

$$\frac{P}{Q}=\frac{R\left(S_1+S_2\right)}{2 S_1 S_2}$$

Answer

$$\frac{P}{Q}=\frac{R\left(S_1+S_2\right)}{S_1 S_2}$$

Answer

$$\frac{P}{Q}=\frac{R\left(S_1 S_2\right)}{S_1+S_2}$$

Current Electricity

In a wheatstone's bridge, three resistances $\mathrm{P}, \mathrm{Q} and \mathrm{R} are connected in the three arms and the fourth arm is formed by two resistances S_1 and S_2$ connected in parallel. The condition for the bridge to be balanced is

Choose the correct answer: