Balance of an alternating current bridge requires that
Answer: A
The balance equation is an equality between two complex products, and a complex equation is two real equations. One fixes the magnitudes and the other the phase angles, so an alternating bridge always needs two independent adjustments worked alternately until the detector falls silent.
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The general balance condition of a four-arm alternating current bridge with arms \( Z_1 \), \( Z_2 \), \( Z_3 \) and \( Z_4 \) taken in order is
Answer: B
It is the same rule as for the Wheatstone bridge with impedances in place of resistances: the products of the opposite arms are equal. Written in polar form it separates at once into equal magnitude products and equal sums of phase angles.
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Expressed in polar form, the balance of an alternating bridge requires that the magnitudes multiply equally and that
Answer: C
With each impedance written as a magnitude at an angle, the two products give \( |Z_1||Z_4| = |Z_2||Z_3| \) together with \( \theta_1 + \theta_4 = \theta_2 + \theta_3 \). The second condition explains why a purely resistive arm cannot balance a purely reactive one.
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If two adjacent arms of an alternating bridge are pure resistances, then to reach balance the remaining two arms must
Answer: D
The two resistive arms contribute zero to each side of the angle equation, so the sum of the angles of the other two must be zero on each side taken separately, which for arms on opposite sides means their angles must be equal. Both must therefore be inductive or both capacitive.
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If two opposite arms of an alternating bridge are pure resistances, the other two arms must be such that
Answer: A
Here one resistive arm falls in each product, so the angle of the remaining arm in one product must equal minus the angle of the remaining arm in the other for the sum to balance. One arm must therefore lag and the other lead, which is why the Maxwell-Wien bridge measures inductance against a capacitance.
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The detector of a bridge working at audio frequency is commonly
Answer: B
The ear is remarkably good at detecting a minimum of tone, and headphones need no supply. Where greater sensitivity or a record is wanted, a tuned amplifier feeding an indicator or an oscilloscope is used instead. A moving coil galvanometer cannot respond to alternating unbalance at all.
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The vibration galvanometer is suitable as a bridge detector because it
Answer: C
Its moving system is mechanically resonant at the supply frequency, so it answers strongly to the fundamental and hardly at all to harmonics or to noise at other frequencies. That selectivity gives a sharp null, but it also confines the instrument to power and low audio frequencies.
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Harmonics in the bridge supply are troublesome because
Answer: D
The balance condition depends on the reactances, which vary with frequency, so a network balanced at the fundamental is not balanced for the harmonics. The residual harmonic voltage keeps the detector from going fully silent, which is why a tuned detector or a filtered source is used.
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Maxwell's inductance bridge compares an unknown inductance with
Answer: A
The unknown coil with its resistance forms one arm and a calibrated variable inductor with a variable resistance forms another, the other two arms being resistances. Two adjustments then bring both parts of the balance condition to zero.
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Maxwell's inductance-capacitance bridge, also called the Maxwell-Wien bridge, measures an inductance in terms of
Answer: B
The unknown inductive arm is balanced against an arm holding a capacitor in parallel with a resistance, which lies diagonally opposite. A capacitance standard is far more stable and far freer from stray fields than a standard inductor, which is the whole reason for the arrangement.
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