1-Phase AC Circuits

Problem 195: What is the wavelength of a carrier wave with a frequency of 100 megahertz?

Problem 196: A chart speed of a recording instrument is 25 mm/sec. One cycle of the signal being recorded extends over 5 mm. What is the frequency of the signal?

Problem 197: A 240-V, 25 Hz sinusoidal generator is connected to a 20 ohms resistor. Determine the instantaneous current when elapsed time is 0.01 second.

Problem 198: A wire carries a current, i = 3 cos 314t amperes. What is the average current over 6 seconds?

Problem 199: Two current sources deliver current to a common load. The first source delivers a current whose equation is 25 sin 100\(\pi\)t amperes while the second delivers a current whose equation is 15 cos 100\(\pi\)t amperes. What is the rms value of the current in the load?

Problem 200: Two alternators A and B delivers 100 and 150 A, respectively to a load. If these currents are out of phase by 30 electrical degrees, determine the total current drawn by the load.

Problem 201: Three loads, units A, B and C are connected in parallel and take currents that are respectively 12, 10 and 15 A respectively. Assuming \(I_a\) to be the reference phasor, \(I_b\) leads \(I_a\) by 30° and \(I_c\) lags behind \(I_a\) by 65°, calculate the total (resultant) current.

Problem 202: An industrial coil has a resistance of 32 ohms and a reactance of 24 ohms and rated 440 volts at 60 Hz. A factory will connect the coil to a 440 V, 50 Hz supply. Solve for the value of a series resistor needed to avoid overcurrent condition.

Problem 203: Across a 230 V, 60 Hz powers supply is a 15-ohm non-inductive resistor. What is the equation of the resulting current?

Problem 204: Two relays each with 20 ohms resistance and 0.16 henry inductance are connected in series. What is the equivalent impedance?

Problem 205: An inductive coil takes a current of 2 A and consumes 160 W when connected to a 240 V AC supply. A second coil when connected across the same supply takes 3 A and 500 W. Find the total power when the two coils are connected in series to this supply.

Problem 206: A 1/2 hp, 110-V, 60 Hz, single-phase induction motor has an efficiency of 88% and a power factor of 0.707 lagging at rated load. This motor is to be connected temporarily on a 220 V, 60 Hz line. Determine the resistance required to be placed in series with the motor in order to prevent the machine from experiencing overcurrent.

Problem 207: Two coils A and B known to have the same resistance are connected in series across a 110-V, 60-cycle line. The current and power delivered by the source are respectively 4.1 A and 300 W. If the voltage across coil A is twice that across coil B, calculate the inductance of coil B.

Problem 208: A coil draws 1875 watts when connected to a 150 V DC source. It consumes 3072 watts when used on 240 V, 60 Hz AC source. Find the inductance of the coil.

Problem 209: A current of 10 A and a power factor of 0.8 lagging is taken from a single phase 250 volt supply. The reactive power of the system is

Problem 210: A resistor of 6 ohms and an unknown impedance coil in series draws 12 A from a 120-V, 60-Hz line. If the real power taken from the line is 1152 watts, what is the coil inductance?

Problem 211: Determine the power angle in the series circuit which consists of R = 25 ohms, L = 0.2 H across a power supply of 200 volts, 30 Hz?

Problem 212: When a 30 V DC source is applied to a given coil, the coil draws 150 W. When 230 V AC is applied to the same coil, it draws 3174 W. Determine the operating power factor of the coil.

Problem 213: The impedance coil absorbs 250 watts when connected across 220 V, 60 Hz mains. It is then connected across 110 V, 25 Hz mains and also absorbs 250 watts. What is the inductance of the coil?

Problem 214: An impedance coil takes 10 A and absorbs 250 W when connected across a 220 V, 60 Hz source. What power will it absorb when connected across 110 V, 25 Hz mains?