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

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

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

Known :

Primary coil (N_P) = 500 loops

Secondary coil (N_s) = 5000 loops

Primary voltage (V_P) = 220 Volt

Wanted : Secondary voltage (V_S)

Solution :

V_s / N_s = V_p / N_p

V_s / 5000 = 220 / 500

V_s / 5000 = 0.44

V_s = (0.44)(5000)

V_s = 2200 Volt

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.

Known :

Primary coil (N_P) = 1200 loops

Secondary coil (N_S) = 1000 loops

The current in the primary coil (I_P) = 4 Ampere

Wanted: The current in secondary coil (I_S)

Solution :

I_S/I_P = N_P/N_S

The current in the secondary coil :

I_S/4 = 1200/1000

I_S/4 = 1.2

I_S = 1.2 (4)

I_S = 4.8 Ampere

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

Known :

Secondary voltage (V_S) = 220 Volt

Primary voltage (V_P) = 110 Volt

Wanted : N_S/N_P

Solution :

V_S/V_P = N_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.

Known :

Secondary voltage (V_S) = 24 Volt

Primary loops (N_P or N₁) = 11 N

Secondary loops (N_{S or} N₂) = 1 N = N

Wanted : Primary voltage (V_P)

Solution :

V_s / N_s = V_p / N_p

24 / N = V_p / 11 N

24 / 1 = V_p / 11

24 = V_p / 11

V_p = (24)(11)

V_p = 264 Volt

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

Known :

Primary coil (N₁) = 21 N

Secondary coil (N₂) = 3 N

Secondary voltage (V₂) = 20 Volt

Wanted : Primary voltage (V₁)

Solution :

V₂ / N₂ = V₁ / N₁

20 / 3 N = V₁ / 21 N

20 / 1 = V₁ / 7

20 = V₁ / 7

V₁ = (7)(20)

V₁ = 140 Volt

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

Known :

Primary voltage (V_P) = 220 Volt

Primary loops (N_P) = 200 loops

Secondary voltage (V_S) = 1100 Volt

Wanted : Secondary loops (N_S)

Solution :

V_s / N_s = V_p / N_p

1100 Volt / N_s = 220 Volt / 200 loops

1100 / N_s = 220 / 200

1100 / N_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.

Known :

Primary voltage (V_P) = 220 Volt

Primary loops (N_P) = 200 loops

Secondary voltage (V_S) = 1100 Volt

Wanted : Secondary loops (N_S)

Solution :

V_s / N_s = V_p / N_p

1100 / N_S = 220 / 200

1100 / N_S = 22 / 20

1100 / N_S = 1.1

N_S = 1100 / 1.1

N_S = 1000

8.

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

Solution :

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

Solution

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.

The correct answer is B.

10.

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

Known :

Primary loops = N_p = 800 loops

Primary voltage =V_P = 220 Volt

Secondary voltage = V_S = 55 Volt

Wanted : Secondary loops (N_S)

Solution :

V_s / N_s = V_p / N_p

55 / N_s = 220 / 800

55 / N_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 < I_p

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

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

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

Solution

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).

The correct answer is B.

1. What is the primary function of a transformer?
   • Answer: 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?
   • Answer: 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?
   • Answer: 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?
   • Answer: 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?
   • Answer: 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?
   • Answer: 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?
   • Answer: 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)?
   • Answer: 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?
   • Answer: 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?

• Answer: 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.