Question

ln a Wheatstone's 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. $ R $
• B. $ 2R $
• C. $ \frac{R}{4} $
• D. $ \frac{R}{2} $

Answer 1

Answer: (A)

The balanced condition of Wheatstone's bridge is
$\frac{R_{A B}}{R_{B C}}=\frac{R_{A D}}{R_{D C}}$
As bridge is in balanced condition, no current will flow through $B D$.

$R_{1} =R_{A B}+R_{B C}$
$=R+R=2 R $
$R_{2} =R_{A D}+R_{C D}=R+R=2 R$
Also, $R_{1}$ and $R_{2}$ are in parallel combination.
Hence, equivalent resistance between $A$ and $C$ will be
$\therefore R_{ eq }=\frac{R_{1} R_{2}}{R_{1}+R_{2}}=\frac{4 R^{2}}{4 R}=R$