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If THE ELECTRIC CIRCUIT 12 [ART. 29 e. Ri be r. 438 e 2 watts. 0433 e 2 watts. 33) = 90 per cent. Prob. 3. The heating element of a 110- volt electric kettle must be = 1 cu. 5 liters (1 liter What at a rate of 10 C. per minute, assuming no losses by radiation. are the resistance of the element and the rated current of the utensil? Ans. 5 amp. + Prob. 4. It is required to calculate the exciting current i, the number n per pole, and the resistance r per turn of a field coil of a 5000-kw. -turns per pole are needed.

What is the frequency of the current in the preceding probr Ans. 50. "^ lem, in cycles per second? Prob. 3. Plot on the same curve sheet with the curve obtained in problem 1 the sine-wave of a current the frequency of which is three times as great, and the amplitude, 52 amp. The curve is to be at its maximum when the first curve is at a maximum. Prob. 4. , and which reaches its positive maxima at the same instants in which the first curve passes through zero. drawn. Show that with these data two distinct curves can be ^ Prob.

6. The current mentioned in problem 1 is generated by a At what 12-pole alternator, that in problem 3 by a 14-pole machine. speeds must these machines be driven in order to give the required Ans. m. frequencies? Prob. 7. Express the currents given in problems 1 to 5 by equa= tions of the form of eq. (36). Ans. i 75 sin u; i = 52 sin 3 u; i = 63 cos u; i = 120 sin (u 30). Prob. 8. The angle u in the answers to the preceding problem is expressed in degrees; rewrite the equations so as to have u expressed in Also represent the currents as funcradians, and in fractions of a cycle.

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