
Problem 
Answer 
1 
An impedance of 5+j8 ohms at 60 cycles is connected in series with a second impedance of 8j0 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 singlephase motors whose impedances at standstill are 2+I_{3}, 4+J_{2}, and l+J_{2} ohms, respectively, are connected in parallel through the same starting switch to a 230volt alternatingcurrent 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 60cycle impedance is 5+j8, is connected in series with a capacitor, whose 60cycle rating at 230 volts is 20 kva, across a 230volt, 60cycle ac 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 noninductive 20ohm resistor across a 220volt 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 120volt 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 aircore inductance coil draws 6 amperes with a power loss of 400 watts when it is connected to a 115volt, 60cycle 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 60cycle impedances of 12+jO, 0  J_{1}2, and 0+j6 connected in series draws 10 amperes from a 60cycle line of 134 volts. How much current would the circuit draw from a 25cycle line of 220 volts? 

18 
An inductive 60cycle susceptance of 0.10 mho is connected in parallel with a conductance of 0.15 mho across a 230volt 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, 3j6, 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 60cycle, 440volt ac line. Calculate the current. 

22 
Calculate the current that would be taken from a 220volt, 25cycle 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 60cycle frequency is applied, the current is 20 amperes. If onehalf of the turns are removed and a voltage of 120 volts of 120cycle 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 60cycle 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, R_{1}  1000 ohms and R_{2} = 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, R_{1} = 20,000 ohms, and R_{2} = 60,000 ohms. Calculate the impedance of the circuit: (a) at 80 cycles per second; (6) at 8000 cycles per second. 
