Question

In a Wheatstone's bridge all the four arms have equal resistance R. If the resistance of the galvanometer is also R, the equivalent resistance of the combination across the battery is

• A. R/2
• B. R
• C. 2R
• D. R/4

Answer 1

The correct option is B R

As Wheatstone bridge is in balanced condition potential difference across AB is zero. We can consider the middle resistor to be short-circuited. Hence resistance across AB does not contribute to effective resistance.
The two resistors R in upper branch are in series. Similarly the two resistors R in lower branch are in series. These two branches having equivalent resistance 2R are in parallel.

So, the equivalent resistance in the circuit is

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

$R_{eq}=R$