Question

In a Whetstone bridge all the four arms have equal resistance R. If the resistance of the galvanometer arm is also R, the equivalent resistance of the combination as seen by the battery is:

• A. 2R
• B. R/4
• C. R/2
• D. R

Answer 1

The correct option is D R

Given: In a Whetstone bridge all the four arms have equal resistance R.

To find the equivalent resistance of the combination as seen by the battery when the resistance of the galvanometer arm is also R

Solution:

This is the case of balanced Wheatstone bridge. The resistance R in galvanometer arm BD is ineffective as $V_B=V_D$. As bridge is in balanced condition, no current will flow through BD.

Resistance of arm ABC=$R+R=2R$

Resistance of arm ADC = $R+R=2R$

These are connected in parallel. Hence the equivalent resistance of the combination is

$=\frac{2R\times 2R}{2R+2R}=R$