Transformer
1. Explain the principle and use of a transformer in an alternating current circuit.
Solution:
A transformer is a device that changes alternating voltage and current to alternating voltage and current of different values, but of the same frequency.
A single-phase transformer has these parts:
- Core made of soft steel (closed)
- Primary coil (N1, U1, I1) connected to the source of alternating current
- Secondary coil (N2, U2, I2) serves as the source of the transformed current and voltage
Transformation ratio:
If ⇒ step-up transformation
If ⇒ step-down transformation
Power in the primary coil
Power in the secondary coil
Transformer efficiency:
2.Complete the table:
Solution:
3.The transformer has N1 = 1000 and N2 = 150 turns. The primary coil is connected to a voltage U1 = 220V and carries a current I1 = 0.3A. What is the voltage and current at the terminals of the secondary coil?
Solution:
Analysis:
At the terminals of the secondary coil, the voltage is U2 = 33V and the current is I2 = 2A.
4.The primary coil of the transformer carries a current of 0.2A at a voltage of 220V. The secondary coil carries a current of 6A and the voltage at the coil terminals is 6.3V. Determine the efficiency of the transformer.
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5.The primary coil of a transformer has 1000 turns, the secondary 1500 turns. The transformer is connected to a harmonic alternating voltage of 220V. What is the voltage at the secondary coil if the transformer is not loaded? What is the voltage at the secondary coil if the resistance of its winding is R2 = 2Ω and it carries a current I2 = 4A?
Please log in to view the solution.6.An induction furnace consists of a transformer whose secondary coil is a single closed turn in the form of a trough into which the material to be melted is placed. Calculate the current flowing in the secondary circuit with a resistance of 0.01Ω. The primary coil connected to the AC source of 240V has 60 turns. What amount of Joule heat is released in the secondary coil in 1 minute?
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7.The primary coil of a transformer has 2400 turns and input power of 2000W. What is the voltage and current in the secondary coil if the transformer has an efficiency η = 90% and the secondary coil has 120 turns? The voltage at the primary coil is 2200V.
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8.The primary coil of a transformer has 2400 turns, a resistance of 120Ω, is connected to AC voltage of 2200V and has an input power of 2000W. The secondary coil has 120 turns and a resistance of 0.05Ω.
- Determine the voltage and current in the secondary coil if η = 90%.
- What energy losses are due to heating of the coils per 1 second?
9.A transformer that transforms voltage from 100V to 3300V has a closed core on which we make one turn using a conductor. With a voltmeter we find out that on this one turn the voltage is 0.5V. How many turns do the transformer coils have?
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10.The power of the transformer is 5kW. What currents flow through the transformer coils connected to the mains voltage of 220V, if U2/U1 = 0.3 holds.
Please log in to view the solution.11.An oil-cooled transformer transformed power P = 10MW with η = 98%. Determine the oil temperature at the outlet of the transformer if its inlet temperature was t = 180C and V/τ = 2.5 l·s-1.
Please log in to view the solution.12.In a loaded transformer, the primary coil is connected to an AC voltage of 220V. The secondary winding has a resistance of 2Ω and a current of 4A flows through it. Determine the voltages on both coils and the thermal losses, assuming N1 = 10000, N2 = 1000.
Please log in to view the solution.13.Electrical energy with power 132kW is to be transmitted from one place to another. The resistance of the conductors is 60Ω. Determine the voltage drop and the power loss in the line if the transmission occurs at 13200V.
Please log in to view the solution.14.Determine the mechanical efficiency of an electric motor that draws a current of 20A at 220V, if it performs work of 144·105 J in one hour.
Please log in to view the solution.15.A transformer reduces voltage from 6000V to 220V. Its power is P = 150kW. Determine the currents in the primary and secondary windings and the transformation ratio k.
Please log in to view the solution.16.Electrical energy with power P = 500kW is to be transmitted via a long-distance line with resistance R = 800Ω. At what voltage will the losses be less than 4%?
Please log in to view the solution.17.Harmonic alternating currents with frequency 50Hz flow through the coils of a single-phase transformer. What is the maximum value of the magnetic induction flux in the transformer core if the effective voltage induced in one turn is 0.25V?
Please log in to view the solution.18.An alternating current with frequency 50Hz flows through the primary coil of a single-phase transformer. In the closed core of the transformer the magnetic induction flux has a maximum value of 2·10–3 Wb. Determine the effective value of the AC voltage induced in the secondary coil with 100 turns.
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19.The primary winding of a transformer has voltage 2kV and current 2A. An electric motor is connected to the secondary coil and operates with power factor 0.82 at 220V. What current does the motor draw from the transformer? What is the motor’s input power?
Please log in to view the solution.20.Two coils A and B are wound on the core of a transformer. If coil A is connected to an AC voltage source, we measure 40/3 V on coil B. If coil B is connected to the same source ( U/B = UA ), we measure 120V on coil A. Determine the transformation ratio.
Please log in to view the solution.21.The transformer of a radio receiver has a cross-section S = 9cm2 and is to be connected to voltage U1 = 220V. Calculate the number of turns of the primary and secondary windings so that it provides voltage U2 = 4V.
