# 10.6: Exercises

- Page ID
- 25026

## Analysis

1. In the magnetic circuit shown in Figure 10.6.1 , assume the cross section is 1 cm by 1 cm with a path length of 8 cm. The entire core is made of sheet steel and there are 100 turns on the winding. Determine the current to establish a flux of 8E−5 webers.

Figure 10.6.1

2. Repeat problem 1 using cast steel for the core.

3. Given the core shown in Figure 10.6.1 , assume the cross section is 2 cm by 2 cm with a path length of 10 cm. The entire core is made of cast steel and there are 200 turns on the winding. Determine the current to establish a flux of 4E−4 webers.

4. Repeat problem 3 using sheet steel for the core.

5. In the magnetic circuit shown in Figure 10.6.1 , assume the cross section is 1 cm by 1 cm with a path length of 8 cm. The entire core is made of sheet steel. Determine the number of turns required to establish a flux of 8E−5 webers given a current of 50 mA.

6. Given the core shown in Figure 10.6.1 , assume the cross section is 2 cm by 2 cm with a path length of 10 cm. The entire core is made of sheet steel Determine the number of turns required to establish a flux of 4E−4 webers given a current of 200 mA.

7. In the magnetic circuit shown in Figure 10.6.2 , assume the cross section is 1 cm by 1 cm. Section A is sheet steel with a path length of 6 cm. Section B is cast steel with a length of 2 cm. There are 500 turns on the winding. Determine the current to establish a flux of 5E−5 webers.

Figure 10.6.2

8. In the magnetic circuit shown in Figure 10.6.2 , assume the cross section is 1 cm by 1 cm. Section A is sheet steel with a path length of 6 cm. Section B is cast steel with a length of 2 cm. Determine the number of turns on the coil to establish a flux of 6E−5 webers with a current of 50 mA.

9. A transformer is shown in Figure 10.6.3 , assume the cross section is 5 cm by 5 cm. The core is sheet steel with a path length of 20 cm. \(N1\) is 500 turns and \(N2\) is 200 turns. Determine the secondary current \((I2)\) if a primary current \((I1)\) of 1 amp establishes a flux of 1.5E−3 webers.

Figure 10.6.3

10. Given the same conditions of problem 9, alter the secondary turns \((N2)\) so that the secondary current \((I2)\) is 3 amps given the original primary current of 1 amp.

11. In general, how would the performance noted in problem 9 change if cast steel was substituted for sheet steel?

12. Given the results of problems 9 through 11, what does the ratio of \(N1\) to \(N2\) represent in terms of idealized performance, and what steps should be taken to make the transformer operate as close to ideal as possible?

13. Given the magnetic circuit shown in Figure 10.6.4 , assume the cross section is 1 cm by 2 cm with a path length of 6 cm. The entire core is made of sheet steel with the exception of a 1 mm air gap. Determine the current required to establish a flux of 4E−4 webers if \(N = 1000\) turns.

Figure 10.6.4

14. Using the data given in problem 13, determine the number of turns required to establish the same flux when the input current is 200 mA.

15. An ideal transformer has a 6:1 voltage step-down ratio. If the primary is driven by 24 VAC and the load is 100 \(\Omega\), determine the load voltage and current, and the primary side current.

16. A 120 VAC transformer is specified as having a 36 volt center-tapped secondary. If each side of the secondary is connected to its own 50 \(\Omega\) load, determine the load currents and the primary side current.

17. An ideal transformer has a 12:1 voltage step-down ratio. If the secondary is connected to a 10 \(\Omega\) load, what impedance is seen from the primary side?

18. An ideal transformer has a 1:5 voltage step-up ratio. If the secondary is connected to a 2 \(\Omega\) load, what impedance is seen from the primary side?

## Design

19. A step-down transformer with \(N=8\) has a 15 volt RMS secondary which is connected to a load with an effective value of 5 \(\Omega\). Determine the minimum acceptable VA rating of the transformer.

20. A step-up transformer with \(N=.5\) is driven from a 120 VAC source. The secondary is connected to a load with an effective value of 150 \(\Omega\). Determine the minimum acceptable VA rating of the transformer.

## Challenge

21. A transformer specified as having a 120 VAC primary with an 18 volt secondary is accidentally connected backwards, with its secondary connected to the source and its primary connected to a 16 \(\Omega\) load. Determine the load current in both the normal and reversed connections. Also determine the required transformer VA rating for both connections.

22. Consider the distributed public address system for an airport as shown in Figure 10.6.5 . It consists of an audio power amplifier with a nominal 70 volt RMS output that is connected to four remote loudspeakers, each separate from the others and some 150 meters away from the amplifier. Each loudspeaker assembly includes a 10:1 voltage step-down transformer that feeds the loudspeaker impedance of 8 \(\Omega\) (resistive) off its secondary. These four lines are fed in parallel by the amplifier. Determine the power delivered to each loudspeaker and the total current delivered by the power amplifier. Assume the transformers are ideal and ignore any cable resistance.

Figure 10.6.5

23. Continuing with the preceding problem, assume that the wiring connecting each transformer back to the amplifier is AWG 22. Determine the power lost in each of the 150 meter long sections of dual cable. Further, suppose the system is reconfigured without the transformers and the output of the amplifier is lowered to 7 volts RMS to compensate. Determine the power lost in each of the cable feeds under the new configuration.

## Simulation

24. Use a transient analysis to verify the results of problem 15.

25. Use a transient analysis to verify the results of problem 16.