Hay’s Bridge: Turanci na Amfani da Ikkarar Zane-zanen Yawancin Kirkiro
Meen Self-Inductance?
Self-inductance yana nufin sifatin da coil ko kofin ke yi wanda yake so haka da zama da karfi ga alamar da yake da shi. Ana ci gaba a henries (H) kuma ana da iya zuwa adadin turns, tsari, da kuma sauran abubuwan da ke samun coil, da kuma permeability na material na core. Self-inductance yana taimaka wajen samun electromotive force (emf) da yake so haka da zama da alamar da yake da shi kamar Lenz’s law.
Meen Faktar Ta Inganci?
Faktar ta inganci yana nufin parametar mai tsarki wanda yake nuna yadda kyau yana da coil ko kofin a resonance da frequency musamman. An kira shi da kuma Q factor ko figure of merit. Ana ci gaba tare da koyar da reactance na coil da resistance na resonant frequency. Q factor masu yawan gaba yana nufin yawan gaba da energy losses da resonance mai sharhi. Q factor zai iya tabbatar da shi a matsayin ratio da energy da ake sake da energy da ake gaza per cycle.
Tsarin Hay’s Bridge
Schematic diagram na Hay’s bridge yana nuna haka:
Kofin yana da four arms: AB, BC, CD, da DA. Arm AB yana da inductor L1 da R1. Arm CD yana da capacitor C4 da R4. Arms BC da DA yana da resistors R3 da R2, respectively. Detector ko galvanometer yana aiki a bayyana balance condition. AC source yana aiki a supply kofin.
Tattalin Arziki na Hay’s Bridge
Balance condition na Hay’s bridge yana faru a lokacin da voltage drops across AB and CD suka duba da zama da opposite, da kuma voltage drops across BC and DA suka duba da zama da opposite. Wannan yana nuna cewa babu current yana haɗa aiki a detector, da kuma deflection yake zero.
Tare da Kirchhoff’s voltage law, za a iya rubuta balance condition haka:
Z1Z4 = Z2Z3
Daga Z1, Z2, Z3, da Z4 su ne impedances na four arms.
Substituting the values of impedances, we get:
(R1 – jX1)(R4 + jX4) = R2R3
where X1 = 1/ωC1 and X4 = ωL4 are the reactances of the inductor and capacitor, respectively.
Expanding and equating the real and imaginary parts, we get:
R1R4 – X1X4 = R2R3
R1X4 + R4X1 = 0
Solving for L1 and R1, we get:
L1 = R2R3C4/(1 + ω2R42C4^2)
R1 = ω2R2R3R4C42/(1 + ω2R42C4^2)
The quality factor of the coil is given by:
Q = ωL1/R1 = 1/ωR4C4
These equations show that L1 and R1 depend on the frequency of the source ω. Therefore, to measure them accurately, we need to know the exact value of ω. However, for high Q factor coils, we can neglect the term 1/ω2R42C4^2 in the denominators and simplify the equations as:
L1 ≈ R2R3C4
R1 ≈ ω2R2R3R4C42
Q ≈ 1/ωR4C4
Phasor Diagram na Hay’s Bridge
Currents I1 and I2 ba su da phase saboda presence na capacitor C4 a arm CD. Current I2 yana lead I1 da angle φ, kamar yadda aka nuna. Voltage drops E1 and E2 suka duba da magnitude da phase saboda suna across pure resistors R1 and R2, respectively. Voltage drops E3, and E4 suka duba da magnitude da phase saboda suna across pure resistors R3 and R4, respectively. Voltage drop E5 yana perpendicular zuwa E4 saboda yana across capacitor C4. Voltage drop E6 yana perpendicular zuwa E1 saboda yana across inductor L1. Phasor diagram yana nuna cewa E6 + E5 = E3 + E4 = E.
Abubuwan Da Ke Gaba Game Da Hay’s Bridge
Hay’s bridge yana bayyana expressions mai sauƙi don kula inductance da resistance na coils da yake da faktar ta inganci.
Hay’s bridge yana bukatar R4 da yake da low value compared to Maxwell’s bridge. Wannan yana rage error due to
