Question

Ra and Rd are the opposite arms of a Wheatstone bridge as are Rc and Rb. The source voltage is applied across Ra and Rc. Then when the bridge is balanced which one of the following is true?

(a) Ra = Rc Rd/Rb

(b) Ra = Rb Rc/Rd

(c) Ra = Rb Rd/Rc

(d) Ra = Rb + Rc + Rd

This question was addressed to me in an online quiz.

My question is based upon Advanced Miscellaneous Problems on Measurement of Resistance in section Measurement of Resistance of Electrical Measurements

Answer 1

Right answer is (b) Ra = Rb Rc/Rd

The explanation is: At balance condition, Potential at B = Potential at D

∴ VA – Ia Ra = VA – Ib Rb

Or, \( \frac{I_a}{I_b}  =  \frac{R_b}{R_a}\)

Similarly,  \( \frac{I_a}{I_b}  =  \frac{R_d}{R_c}\)

∴ Ra = \( \frac{R_b R_c}{R_d}\).