An alternating-current bridge that measures mutual inductance. Direct comparison of a mutual inductance with a standard mutual inductance is virtually impossible because effects, such as the self- and mutual capacitances of the coils, produce voltage components in the secondary circuits in phase with the primary current. This problem is overcome in the Hartshorn bridge by the use of a variable resistor, of resistance r, common to both the primary and secondary circuits of the bridge (see diagram). The standard inductance and the resistance are varied until a balance is achieved with no response registered by the indicating instrument I; assuming that the secondaries are connected in antiphase, then

where ρ₁ and ρ₂ are the resistances of the mutual inductances M₁ and M₂.

Hartshorn bridge