Step-up and step-down transformer – problems and solutions

Step-up and step-down transformer – problems and solutions

1. يو ترانسفارمر has a primary coil and a secondary coil with the number of loops are 500 and 5000. Input ولټيج is 220 V. What is the output voltage?

پیژندل شوی:

Primary coil (N_P) = 500 loops

Secondary coil (N_s) = 5000 loops

Primary voltage (V_P) = ۲۲۰ ولټه

غوښتل شوي: Secondary voltage (V_S)

حل:

V_s / ن_s = وی_p / ن_p

V_s / ۲۵۰ = ۴ / ۱۰

V_s / ۲۵۰ = ۰.۴

V_s = (۰.۴۴)(۵۰۰۰)

V_s = ۲۲۰۰ ولټه

2. A transformer has primary coil with 1200 loops and secondary coil with 1000 loops. If the current in the primary coil is 4 Ampere, then what is the the current in the secondary coil.

پیژندل شوی:

Primary coil (N_P) = 1200 loops

Secondary coil (N_S) = 1000 loops

The current in the primary coil (I_P) = ۴ امپیرونه

SE busca: The current in secondary coil (I_S)

حل:

I_S/I_P = ن_P/N_S

The current in the secondary coil :

I_S/4 = 1200/1000

I_S/4 = 1.2

I_S = ۱.۲ (۴)

I_S = ۴.۸ امپیرونه

3. The secondary voltage is 220 Volt and primary voltage is 110 volt, then a comparison of the secondary coil and primary coil is…

پیژندل شوی:

Secondary voltage (V_S) = ۲۲۰ ولټه

Primary voltage (V_P) = ۲۲۰ ولټه

غوښتل شوي: N_S/N_P

حل:

V_S/V_P = ن_S/N_P

220/110 = N_S/N_P

22/11 = N_S/N_P

2/1 = N_S/N_P

12/6 = N_S/N_P

4. Based on figure below, what is the primary voltage of the transformer.

پیژندل شوی:

Secondary voltage (V_S) = ۲۲۰ ولټه

Primary loops (N_P یا ن₁) = ۱۱ ن

Secondary loops (N_{س یا} N₂) = ۱ ن = ن

غوښتل شوي: Primary voltage (V_P)

حل:

V_s / ن_s = وی_p / ن_p

۲۴ / ن = وی_p / ۱۱ ن

۲۴ / ۱ = وی_p / 11

۲۴ = وی_p / 11

V_p = (۰.۴۴)(۵۰۰۰)

V_p = ۲۲۰۰ ولټه

5. Based on figure below, what is the input voltage of the ترانسفارمر.

پیژندل شوی:

Primary coil (N₁) = ۱۱ ن

Secondary coil (N₂) = ۱۱ ن

Secondary voltage (V₂) = ۲۲۰ ولټه

غوښتل شوي: Primary voltage (V₁)

حل:

V₂ / ن₂ = وی₁ / ن₁

20 / 3 N = V₁ / ۱۱ ن

۲۴ / ۱ = وی₁ / 7

۲۴ = وی₁ / 7

V₁ = (۰.۴۴)(۵۰۰۰)

V₁ = ۲۲۰۰ ولټه

6. According to figure below, what is the amount of the secondary loops of the transformer.

پیژندل شوی:

Primary voltage (V_P) = ۲۲۰ ولټه

Primary loops (N_P) = 200 loops

Secondary voltage (V_S) = ۲۲۰ ولټه

غوښتل شوي: Secondary loops (N_S)

حل:

V_s / ن_s = وی_p / ن_p

۱۱۰۰ ولټه / ن_s = 220 Volt / 200 loops

1100 / ن_s = 220/200

1100 / ن_s = 1.1

N_s = 1100/1.1

N_s = 1000 loops

7. According to figure below, what is the amount of the secondary loops of the transformer.

پیژندل شوی:

Primary voltage (V_P) = ۲۲۰ ولټه

Primary loops (N_P) = 200 loops

Secondary voltage (V_S) = ۲۲۰ ولټه

غوښتل شوي: Secondary loops (N_S)

حل:

V_s / ن_s = وی_p / ن_p

1100 / ن_S = 220/200

1100 / ن_S = 22/20

1100 / ن_S = 1.1

N_S = 1100/1.1

N_S = 1000

8.

بدلون	Np	Ns	Vp	Vs	Ip	Is
1	1000		120	12	0.4	2
2	80	8	20	2		2.5

Based on the above table, if the efficiency of both transformers is the same, 50%, Determine N_s او زه_p.

حل:

The equation of transformer’s efficiency :

Calculate N_s of the transformer 1 :

Calculate I_p of the transformer 2 :

9.

Based on the above figure, which of the following statements about the figure above is correct.

A. Figure 1 is a step-up transformer and figure 2 is a step-down transformer

B. Figure 1 is a step-down transformer and figure 2 is a step-up transformer

C. Figure 1 and 2 are a step-down transformer

D. Figure 1 and 2 are a step-up transformer

د حل

Step-up transformer serves to raise the electrical voltage while the step-down transformer to reduce electrical voltage. In Figure 1, the primary voltage is greater than the second voltage (20 Volts > 5 Volts) so that Figure 1 is a step-down transformer. In Figure 2, the primary voltage is smaller than the second voltage (5 Volts < 40 Volts) so that Figure 2 is a step-up transformer.

سم ځواب ب دی.

10.

If the primary coil has 800 loops, then determine the secondary coil.

پیژندل شوی:

Primary loops = N_p = 800 loops

Primary voltage =V_P = ۲۲۰۰ ولټه

Secondary voltage = V_S = ۲۲۰۰ ولټه

غوښتل شوي: Secondary loops (N_S)

حل:

V_s / ن_s = وی_p / ن_p

55 / ن_s = 220/800

55 / ن_s = 22/80

N_S = (80)(55) / 22

N_S = 4400/22

N_S = 200 loops

11.

The correct statement about transformer P and Q is…

A. P is a step-down transformer because of I_s < زه_p

B. P is a step-up transformer because of V_p < وي_s

C. Q is a step-up transformer because of V_p > وي_s

D. Q is a step-up transformer because I_s > I_p

د حل

P is step-up transformer because primary voltage (V_p = 110 V) < secondary voltage (V_s = 200 V).

Q is step-down transformer because primary voltage (V_p = 220 V) > secondary voltage (V_s = 110 V).

سم ځواب ب دی.

1. What is the primary function of a transformer?
   • ځواب: The primary function of a transformer is to change the voltage of an alternating current (AC) electrical power source. This is done by increasing (step-up) or decreasing (step-down) the voltage based on the application’s needs.
2. How do step-up and step-down transformers differ in their function?
   • ځواب: A step-up transformer increases the voltage from the primary to the secondary coil, while a step-down transformer decreases the voltage from the primary to the secondary coil.
3. What is the relationship between the number of turns in the primary and secondary coils of a transformer and its voltage transformation?
   • ځواب: The voltage transformation ratio is directly proportional to the turns ratio. If the secondary coil has more turns than the primary coil, it’s a step-up transformer, and vice versa. The voltage in each coil is proportional to the number of turns in that coil.
4. Why is there a need to step up the voltage for transmitting electrical power over long distances?
   • ځواب: Stepping up the voltage reduces the current for a given power, which in turn reduces resistive power losses in transmission lines. Lower current also means thinner wires can be used, which are cheaper and easier to manage.
5. Why do homes typically receive electricity at a much lower voltage than that used for transmission?
   • ځواب: Higher voltages, while efficient for transmission, are dangerous for domestic use. Thus, before electrical power enters homes, step-down transformers are used to reduce the voltage to safer levels for household appliances and electronics.
6. Is energy lost when electricity is transformed from one voltage to another in a transformer?
   • ځواب: Ideal transformers would have no energy loss, but real transformers do have losses. These losses are mainly due to resistive heating in the coils and magnetic losses in the core. However, transformers are generally very efficient, often above 90-95%.
7. What is the importance of the transformer core material?
   • ځواب: The core material plays a significant role in the efficiency and function of the transformer. It’s typically made of iron or ferrite, which helps guide the magnetic flux between the primary and secondary coils. The core material’s properties affect the transformer’s efficiency, magnetic losses, and ability to carry the flux without getting saturated.
8. Can transformers work with direct current (DC)?
   • ځواب: No, transformers require a changing magnetic flux to induce voltage, which is provided by alternating current (AC). With direct current (DC), once the current stabilizes, there’s no changing flux, and thus, no voltage is induced in the secondary coil.
9. Why might a step-down transformer be used in electronic devices like chargers?
   • ځواب: Many electronic devices operate at lower voltages than the standard household supply. A step-down transformer in a charger or adapter reduces the voltage to a level suitable for the device, ensuring it operates safely and efficiently.
10. How do changes in load (like using more or fewer appliances) affect the output voltage of a transformer?

• ځواب: In an ideal transformer, changes in load would not affect the output voltage. However, in real transformers, due to internal resistances and reactances, the output voltage can drop slightly under high load conditions and rise slightly under low load conditions.