Question

The circuit shown in the figure below, called the Wheatstone bridge, is used to determine the value of unknown resistor Xby comparison with three resistors M, N, and P whose resistances can be varied. For each setting, the resistance of each resistor is precisely known. With switches K₁ and K₂ closed, these resistors are varied until the current in the galvanometer G is zero; the bridge is then said to be balanced.

(a) Show that under this condition the unknown resistance is given by X = MP/N. (This method permits very high precision in comparing resistors.) (Do this on paper. Your instructor may ask you to turn in this work.)

(b) If the galvanometer G shows zero deflection when M = 829.0 Ω, N = 15.20 Ω, and P = 33.48 Ω, what is the unknown resistance X?
Ω

Answer 1

Zero current through the galvanometer means the current I1 through N is also the current through M and the current I2 through P is the same as the current through X. And it means that points b and c are at the same potential,

so I1*N = I2*P.

The voltage between points a and d is E

I1 = E/(N+M)

I2 = E/(P+X)

I1*N = I2*P

(E/(N+M))*N = ( E/(P+X))*P

N*(P+X) = P(N+M)

NX = PM

X = PM/N

B.

X = 33.48*829/(15.20) = 1825.98 ohm