# 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 N_{1}) = 11 N

Secondary loops (N_{S or} N_{2}) = 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 (N_{1}) = 21 N

Secondary coil (N_{2}) = 3 N

Secondary voltage (V_{2}) = 20 Volt

__Wanted :__ Primary voltage (V_{1})

__Solution :__

V_{2 }/ N_{2} = V_{1} / N_{1}

20 / 3 N = V_{1} / 21 N

20 / 1 = V_{1} / 7

20 = V_{1} / 7

V_{1} = (7)(20)

V_{1} = 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.

Transformer | 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} 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.