AC Bridges Questions and Answers

Answer: A

Magnitude balance requires the products of opposite pairs to be equal, so \( 200 \times Z = 400 \times 100 \) and \( Z = 200\ \Omega \). The phase condition is a separate equation and must be satisfied at the same time before the detector goes silent.

Answer: B

Opposite arms are the first with the fourth and the second with the third, so the condition is \( \theta_1 + \theta_4 = \theta_2 + \theta_3 \). Rearranging gives \( \theta_4 = -10 + 50 - 30 = +10^\circ \). The magnitude condition must hold at the same time before the detector will fall silent.

Answer: C

The loss is \( \omega C V^2 \tan\delta \), that is \( 314.2 \times 0.2 \times 10^{-6} \times 10^{8} \times 0.005 \), which comes to about 31 watts. Without the loss tangent the same product gives 6.3 kVAr, the reactive power the specimen draws, which is not dissipated at all.

Answer: D

The balance equation is complex and therefore stands for two real equations, one in magnitude and one in phase. Two independent controls are needed and they are worked alternately, each disturbing the other, until the detector is silent.

Answer: A

Inductance appears on both sides of the balance equation and the frequency factor cancels, so the result is free of it. That is a real convenience, since a mains-derived supply drifts. Bridges involving a capacitance against an inductance can also be arranged so that frequency cancels.

Answer: B

The whole point of testing at high voltage is that the loss tangent of a defective specimen rises with the applied stress, as voids begin to discharge. A tip-up curve of loss tangent against voltage is a standard diagnostic, so the test voltage is an essential part of the result.

Answer: C

The ear is insensitive at 50 hertz, so the null cannot be judged. A vibration galvanometer tuned to the supply frequency is used instead at power frequencies, while headphones come into their own between about five hundred and two thousand hertz where hearing is acute.

Answer: D

A standard inductor couples to whatever lies near it and changes value with the metal in its vicinity, while a capacitor's field is confined between its plates. That single property is why inductance is measured against capacitance rather than against a standard coil.

Answer: A

The alternate adjustment is needed because the two nulls interact, not because a corner earth would short an arm. Earthing one corner is in fact perfectly possible; it simply leaves the stray capacitances of the other corners in parallel with the arms, which is what the Wagner branch is designed to avoid.

Answer: B

A network balanced for the fundamental is not balanced for the third or fifth harmonic, because each arm's reactance is different at those frequencies. The residual harmonic voltage keeps the detector alive, and the cure is a tuned detector or a cleaner source.