The instrument used to measure resistance is the Wheatstone bridge with a slide resistance-a wire of high resistivity of length L (Fig. 26.6). Here R is a calibrated resistance, `R_x,` the unknown resistance. By moving the sliding contact, the current in the galvanometer is made to
drop to zero. Making use of this condition (of bridge balance), find the resistance being measured.

Answer

`R_x=Rl_(1)//l_(2)=Rl//(L-l)`, where L=AB, l=BD`

Explanation

In a balanced bridge the current flowing through the galvonometer is zero, so `omega_(c )=Psi_(D)`. According to Ohm.s law for a homogeneous section, we have `Psi_(A)-Psi_(c )=IR, Psi_(c )-Psi_(B)=IR_(x), Psi_(A)-Psi_(D)=IR_(1)=ipl_(1)//S, Psi_(D)-Psi_(B)=iR_(2)=ipl_(2)lS`. Hence we find the unknown resistance.