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

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)  (R/4)  (D)  (R/2)

Tardigrade Admin · Accepted Answer

The balanced condition of Wheatstone's bridge is

\frac{R _{A B}}{R _{BC}} = \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_{BC}

= 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

∴ R_{e q} = \frac{R _{1} R _{2}}{R _{1} + R _{2}} = \frac{4 R ^{2}}{4 R} = R

Q. 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

$R$

$2 R$

$\frac{R}{4}$

$\frac{R}{2}$

Q. 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

R

2R

4R​

2R​

Q. 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

$R$

$2 R$

$\frac{R}{4}$

$\frac{R}{2}$