AC Bridges Questions and Answers

41.

A Schering bridge at 50 Hz balances with \( C_4 = 0.5\ \mu \)F and \( R_4 = 637\ \Omega \). Using \( \tan\delta = \omega C_4 R_4 \), the dissipation factor of the specimen is about

A.0.32
B.1.0
C.0.10
D.0.016

Answer: C

The angular frequency is 314.2 radians per second, and \( 314.2 \times 0.5 \times 10^{-6} \times 637 = 0.100 \). A loss tangent of a tenth is high for sound insulation, where a few thousandths would be usual, so such a specimen would be viewed with suspicion.

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42.

If the dissipation factor of a specimen measured on a Schering bridge is 0.04 at 50 Hz, then at 100 Hz with the same arm settings the bridge would indicate

A.0.04
B.0.02
C.0.16
D.0.08

Answer: D

The expression \( \tan\delta = \omega C_4 R_4 \) is directly proportional to frequency, so with the arms unchanged the indication doubles. This is why the test frequency must always be quoted alongside a loss tangent, and why readings at different frequencies cannot be compared directly.

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43.

Three arms of an alternating bridge have impedance magnitudes of 200, 400 and 100 ohms, the last two being opposite each other. For magnitude balance the fourth arm, opposite the first, must be

A.200 \( \Omega \)
B.800 \( \Omega \)
C.50 \( \Omega \)
D.100 \( \Omega \)

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.

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44.

In a bridge with arms \( Z_1 \), \( Z_2 \), \( Z_3 \) and \( Z_4 \) taken in order, the phase angles of the first three are \( +30^\circ \), \( -10^\circ \) and \( +50^\circ \). For balance the angle of the fourth arm must be

A.\( +70^\circ \)
B.\( +10^\circ \)
C.\( +90^\circ \)
D.\( -30^\circ \)

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.

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45.

A cable specimen measured on a Schering bridge gives a capacitance of 0.2 \( \mu \)F and a loss tangent of 0.005 at 50 Hz. Its dielectric loss on a 10 kV test is about

A.3.1 W
B.0.31 W
C.31 W
D.6.3 kW

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.

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46.

True or false: an alternating current bridge can be balanced by a single adjustment.

A.True, provided all four arms of the bridge are made of pure resistances alone
B.True, since the detector responds only to the magnitude of the unbalance voltage
C.True, if the supply frequency is chosen so that the reactances cancel of themselves
D.False, two independent controls are needed for magnitude and phase

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.

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47.

True or false: the balance of Maxwell's inductance bridge depends on the supply frequency.

A.False, the frequency cancels from the balance equation
B.True, because the reactance of the unknown coil rises with the frequency of the supply
C.True, since the standard inductor changes value as the frequency is altered
D.True, and the frequency must therefore be quoted with every result obtained from it

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.

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48.

True or false: a Schering bridge measures the dissipation factor without regard to the voltage at which the test is made.

A.True, because balance is a null condition and a null cannot depend on amplitude
B.False, the loss tangent of a faulty specimen rises with stress
C.True, since the dissipation factor is a ratio and ratios are independent of voltage
D.True, provided the standard capacitor is rated for the voltage being applied

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.

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49.

True or false: headphones are useless as a bridge detector at power frequency.

A.False, provided the headphones are of the high-impedance type used in bridge work
B.True, because headphones respond only to the direct component of the unbalance
C.True, since fifty hertz is too low for the ear to judge a minimum
D.False, the ear being equally sensitive at all frequencies from twenty hertz upward

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.

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50.

Assertion: a capacitance standard is preferred to an inductance standard in precision bridge work. Reason: a capacitor has no external magnetic field and suffers no eddy current loss.

A.both the assertion and the reason are true but the reason does not explain the assertion
B.the assertion is true but the reason given for it is false
C.the assertion is false although the reason offered is a true statement in itself
D.both the assertion and the reason are true and the reason explains the assertion

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.

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