Problems

Author: E.E. Kimberly

	Problem	Answer
1	An impedance of 5+j8 ohms at 60 cycles is connected in series with a second impedance of 8-j0 ohms at 60 cycles across an alternating voltage of 230 volts at 60 cycles. Calculate the current. Ans. 15.1 amp
2	Calculate the current that would flow if the two impedances of Problem 1 were connected in series across a line whose direct voltage is 230 volts.
3	Three single-phase motors whose impedances at standstill are 2+I3, 4+J2, and l+J2 ohms, respectively, are connected in parallel through the same starting switch to a 230-volt alternating-current line. Calculate the current in the line at start.	210 amp
4	Calculate the voltage applied to each impedance in Problem 1.
5	How many ohms of pure capacitive reactance must be connected in parallel with the load of Problem 3 to correct its power factor to 100%?
6	A reactor, whose 60-cycle impedance is 5+j8, is connected in series with a capacitor, whose 60-cycle rating at 230 volts is 20 kv-a, across a 230-volt, 60-cycle a-c line. Calculate the voltage across the capacitor.
7	Calculate the active power, the apparent power, and the reactive power in Problem 3.
8	A condenser with a capacitance of 200 mf is connected in series with a non-inductive 20-ohm resistor across a 220-volt line. Determine the current that will flow at each of the following frequencies: 30, 40, 50, and 60 cycles. What is the voltage drop across each part of the circuit at 60 cycles? What is the power factor of the circuit in each case?
9	In starting a certain automobile, the starting motor draws 140 amperes (average) for 4 seconds. How many coulombs of electricity pass through the motor?
10	A condenser has a reactance of 10 ohms at 25 cycles. Calculate its capacitance.
11	A condenser has a capacitance of 0.0002 farad. What voltage at 40 cycles would produce 5 amperes of current in it?
12	A condenser of 0.00212 farad takes 4 amperes from a 120-volt line. What is the line frequency?
13	In Problem 11, how much energy per cycle is exchanged between the condenser and the supply?
14	How many farads of capacitance would be required in a condenser to produce the same reactance in ohms on 60 cycles as does a pure inductance of 0.1 henry on 40 cycles?	106 µF
15	An air-core inductance coil draws 6 amperes with a power loss of 400 watts when it is connected to a 115-volt, 60-cycle supply. If the frequency were reduced to 25 cycles, how many volts would be required to produce the same power loss?
16	A pure resistance of 5 ohms and a pure reactance of 10 ohms are connected in parallel to a voltage of 100+jO volts. Write the complex expression for the current.
17	A circuit containing 60-cycle impedances of 12+jO, 0 - J12, and 0+j6 connected in series draws 10 amperes from a 60-cycle line of 134 volts. How much current would the circuit draw from a 25-cycle line of 220 volts?
18	An inductive 60-cycle susceptance of 0.10 mho is connected in parallel with a conductance of 0.15 mho across a 230-volt supply. What are the line current and the angle by which it lags the line voltage?
19	What is the angle of displacement between two voltages whose complex expressions are 0+j50 and 5+j80?
20	A voltage of 125 volts is applied to a circuit containing three impedances of 4+j5, 3-j6, and 4+j0 in series. Write the complex expression for the voltage across the reactor.
21	Five condensers of 0.0012 farad each are connected in series across a 60-cycle, 440-volt a-c line. Calculate the current.
22	Calculate the current that would be taken from a 220-volt, 25-cycle line by the five condensers of Problem 21 connected in parallel.
23	A coil of 1000 turns of wire is wound on a wooden ring. When a voltage of 240 volts of 60-cycle frequency is applied, the current is 20 amperes. If one-half of the turns are removed and a voltage of 120 volts of 120-cycle frequency is applied, how much current will flow? Assume negligible resistance.	20 amp
24	A wire solenoid has a power loss of 200 watts when a voltage of 240 volts of 60-cycle frequency is applied and a current of 2 amperes flows. What voltage at a frequency of 25 cycles must be applied to produce the same power loss?	135 volts
25	Two resistors, R1 - 1000 ohms and R2 = 20,000 ohms, are connected in series. How many microfarads of capacitance must be connected across Ri to reduce the impedance across Ri to 100 ohms, if the frequency / is 60 cycles per second? How many, f= 400,000?
26	In the circuit shown in the diagram, C = 0.1 mf, R1 = 20,000 ohms, and R2 = 60,000 ohms. Calculate the impedance of the circuit: (a) at 80 cycles per second; (6) at 8000 cycles per second.