71 
The resistance of the winding in each of the saturable reactors of Example 71 is 35 ohms and the resistance of the noninductive load is 140 ohms.
Calculate
 The max value of the current.
 The rms value of the current.
 The power output.
 The efficiency of the frequency tripler. Neglect core losses.

72 
Explain why a magnetic frequency multiplier operating on the principles discussed in Section 71 requires an odd number rather than an even number of saturable reactors.

73 
A 120v, 60cycle, singlecore saturable reactor has a dc control winding of 900 turns and an ac output winding of 225 turns. The load is a noninductive resistance of 59.5 ohms and the resistances are R_{c} = 10.0 ohms and R_{G} = 0.5 ohm for the control winding and output winding respectively. Assume the ac flux density to be just below the saturated value and calculate the selfinductance of a choke in the control circuit such that the alternating current induced in the control winding is not to exceed 0.25 amp when the premagnetization is zero. Neglect the resistance of the control circuit.

74 
Calculate the amplitude of the flux when the saturable reactor of Problem 73 is operated in series with the 59.5ohm resistor from a 120v, 60cycle source with its control circuit opencircuited. Assume the shape of the magnetization curve in Fig. 73(b) for the core material.

75 
Plot the wave form of the output current if the saturable reactor in Problems 73 and 74 is operated in series with the 59.5ohm resistor from a 130v, 60cycle source with its control circuit opencircuited. What is the amplitude of the current?

76 
Assume the choke in the control circuit of the saturable reactor in Problems 73 and 74 to have infinite inductive reactance.
 Calculate the output current if the premagnetization is of a value such that the core remains saturated throughout the entire voltage cycle, while the reactor is operated with its connected load from a 120v, 60cycle source.
 What is the minimum value of premagnetizing current for this condition?

77 
 Calculate the angle α_{2} at which the saturable reactor of Problems 73
and 74 becomes unsaturated when supplying the 59.5ohm resistance load from a 120v, 60cycle source with a control current of 0.354 amp.
 Estimate the value of the firing angle at. Assume an infinite choke in the control circuit.

78 
The core in the reactor of Problem 74 has a net crosssectional area of 2.25 sq in. and a mean length of 11.75 in. Assume the hysteresis loop to be rectangular and the coercive force to be 72 amp turns per m for the material in the core, and calculate the current when the reactor operates with its connected load of 59.5 ohms from a 120v, 60cycle source with zero premagnetization, Plot the approximate wave form of the current.

79 
The saturable reactor of Problems 73 and 74 is to operate from a 400cycle system with the amplitude of the ac flux just below the saturated value at zero premagnetization. Calculate
(a) The voltage of the source.
(b) The value of the noninductive load resistance if the current range is to be the same as for 60cycle operation. What is the ratio of maximum power output to that for 60cycle operation?

710 
The saturable reactor of Problems 73 and 74 is to be rewound for operation at 120 v and 400 cps with the load specified in Problem 73.
(a) What changes, if any, should be made in one or both windings?
(b) How would the current rating be changed?
(c) How does the power output rating compare with that of Problem 79?

711 
The cores in a 2core saturable reactor are toroids of the following dimensions: ID = 2 1/2in., OD = 5 in., and height = 2 in. The stacking factor is 0.80. The number of turns N_{C} in the control winding on each core is 900 turns. The core is assumed to saturate abruptly at B_{s} = 90000 lines per sq in. and the magnetization curve to be horizontal in the saturated region and vertical in the unsaturated region. The control windings are connected in series. The gate windings are connected in parallel for operation from a 120v, 60cycle source. The rated value of the output current is 2 amp (average value, not rms). Calculate
(a) The number of turns in each gate winding if the flux density is just below saturated value at zero premagnetization.
(b) The rms value of rated current.
(c) The resistance of the load if the firing angle α is zero at rated output for a 60cycle emf of 120 v if the resistance of the gate windings is neglected.
(d) The average value and rms value of the rated current of the control winding on the basis of (c).

712 
The 2core saturable reactor in Problem 711 is delivering rated current at 120 v, 60 cps to a noninductive resistance of 50 ohms. The resistance of the gate windings may be neglected. Calculate
(a) The firing angle α.
(b) The control current.
(c) The output current if the control current remains at the value in (b) while the load resistance is reduced to 10 ohms.
(d) The firing angle α for (c).
(e) The form factor for (a) and (c).

713 
The reactor in Problem 712 is operating with a choke in its control circuit of such size that the free evenharmonics in the control circuit are negligible.
Neglect the resistance of the gate windings and calculate
(a) The maximum value of resistance for rectangular wave form of output current from a 120v, 60cycle supply.
(b) The voltage across the choke in the control circuit.

714 
A 2core saturable reactor is used in an arc welder. The number of turns on each core are N_{C} = 300 and N_{G} = 20. The gate windings are seriesconnected and supplied from a 90v, 60cycle source. The control windings are also seriesconnected and receive their current from a 30v dc source with a potentiometer voltage divider to adjust the control current. The voltage across the welding arc is nearly constant at 25 v rms. Calculate
(a) The dc value of the control current for a welding current of 200 amp rms. (Assume sinusoidal current wave form.)
(b) The rms value of the control current.
(c) The amplitude of the voltage wave if the impedance of the control circuit is negligible.
(d) The power gain if the voltage applied to the control windings is 28 v and the arc voltage is 25 v. Neglect losses in the voltage divider and assume the arc voltage to be in phase with the arc current.
(e) The ampere turn gain.
(f) The current gain.

715 
A dc transformer, as shown in Fig. 711(d), for measuring direct currents up to 2000 amp has a rated output of 1 amp dc.
(a) Calculate the number of turns in each gate winding.
(b) The ac supply is 120 v, 60cps. Estimate the crosssectional area of the core in square inches. Assume a stacking factor of 0.80.
