{"id":1731,"date":"2018-04-05T12:31:45","date_gmt":"2018-04-05T04:31:45","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=1731"},"modified":"2023-08-10T00:08:38","modified_gmt":"2023-08-10T00:08:38","slug":"step-up-and-step-down-transformer-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/step-up-and-step-down-transformer-problems-and-solutions.htm","title":{"rendered":"Step-up and step-down transformer \u2013 problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

Step-up and step-down transformer \u2013 problems and solutions<\/span><\/p>\n

1. A transformer<\/a> has a primary coil and a secondary coil with the number of loops are 500 and 5000. Input voltage<\/a> is 220 V. What is the output voltage?<\/span><\/p>\n

Known :<\/u><\/span><\/p>\n

Primary coil (NP<\/sub>) = 500 loops<\/span><\/p>\n

Secondary coil (Ns<\/sub>) = 5000 loops<\/span><\/p>\n

Primary voltage (VP<\/sub>) = 220 Volt<\/span><\/p>\n

Wanted :<\/u> Secondary voltage (VS<\/sub>)<\/span><\/p>\n

Solution :<\/u><\/span><\/p>\n

Vs <\/sub>\/ Ns <\/sub>= Vp<\/sub> \/ Np<\/sub><\/span><\/p>\n

Vs <\/sub>\/ 5000 = 220 \/ 500<\/span><\/p>\n

Vs <\/sub>\/ 5000 = 0.44<\/span><\/p>\n

Vs <\/sub>= (0.44)(5000) <\/span><\/p>\n

Vs<\/sub> = 2200 Volt<\/span><\/p>\n

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.<\/span><\/p>\n

Known :<\/u><\/span><\/p>\n

Primary coil (NP<\/sub>) = 1200 loops<\/span><\/p>\n

Secondary coil (NS<\/sub>) = 1000 loops<\/span><\/p>\n

The current in the primary coil (IP<\/sub>) = 4 Ampere<\/span><\/p>\n

Wanted:<\/u> The current in secondary coil (IS<\/sub>)<\/span><\/p>\n

Solution :<\/u><\/span><\/p>\n

IS<\/sub>\/IP<\/sub> = NP<\/sub>\/NS<\/sub><\/span><\/p>\n

The current in the secondary coil :<\/span><\/p>\n

IS<\/sub>\/4 = 1200\/1000<\/span><\/p>\n

IS<\/sub>\/4 = 1.2<\/span><\/p>\n

IS <\/sub>= 1.2 (4)<\/span><\/p>\n

IS <\/sub>= 4.8 Ampere<\/span><\/p>\n

3. The secondary voltage is 220 Volt and primary voltage is 110 volt, then a comparison of the secondary coil and primary coil is…<\/span><\/p>\n

Known :<\/u><\/span><\/p>\n

Secondary voltage (VS<\/sub>) = 220 Volt<\/span><\/p>\n

Primary voltage (VP<\/sub>) = 110 Volt<\/span><\/p>\n

Wanted :<\/u> NS<\/sub>\/NP<\/sub><\/span><\/p>\n

Solution :<\/u><\/span><\/p>\n

VS<\/sub>\/VP <\/sub>= NS<\/sub>\/NP<\/sub><\/span><\/p>\n

220\/110 = NS<\/sub>\/NP<\/sub><\/span><\/p>\n

22\/11 = NS<\/sub>\/NP<\/sub><\/span><\/p>\n

2\/1 = NS<\/sub>\/NP<\/sub><\/span><\/p>\n

12\/6 = NS<\/sub>\/NP<\/sub><\/span><\/p>\n

4. Based on figure below, what is the primary voltage of the transformer.<\/span><\/p>\n

Known :\"Stepa-up<\/u><\/span><\/p>\n

Secondary voltage (VS<\/sub>) = 24 Volt<\/span><\/p>\n

Primary loops (NP<\/sub> or N1<\/sub>) = 11 N<\/span><\/p>\n

Secondary loops (NS or<\/sub> N2<\/sub>) = 1 N = N<\/span><\/p>\n

Wanted :<\/u> Primary voltage (VP<\/sub>)<\/span><\/p>\n

Solution :<\/u><\/span><\/p>\n

Vs <\/sub>\/ Ns<\/sub> = Vp<\/sub> \/ Np<\/sub><\/span><\/p>\n

24 \/ N = Vp<\/sub> \/ 11 N<\/span><\/p>\n

24 \/ 1 = Vp<\/sub> \/ 11<\/span><\/p>\n

24 = Vp<\/sub> \/ 11<\/span><\/p>\n

Vp <\/sub>= (24)(11)<\/span><\/p>\n

Vp<\/sub> = 264 Volt<\/span><\/p>\n

5. Based on figure below, what is the input voltage of the transformer<\/a>.<\/span><\/p>\n

Known :\"Step-up<\/u><\/span><\/p>\n

Primary coil (N1<\/sub>) = 21 N<\/span><\/p>\n

Secondary coil (N2<\/sub>) = 3 N<\/span><\/p>\n

Secondary voltage (V2<\/sub>) = 20 Volt<\/span><\/p>\n

Wanted :<\/u> Primary voltage (V1<\/sub>)<\/span><\/p>\n

Solution :<\/u><\/span><\/p>\n

V2 <\/sub>\/ N2<\/sub> = V1<\/sub> \/ N1<\/sub><\/span><\/p>\n

20 \/ 3 N = V1<\/sub> \/ 21 N<\/span><\/p>\n

20 \/ 1 = V1<\/sub> \/ 7<\/span><\/p>\n

20 = V1<\/sub> \/ 7<\/span><\/p>\n

V1<\/sub> = (7)(20) <\/span><\/p>\n

V1<\/sub> = 140 Volt<\/span><\/p>\n

6. According to figure below, what is the amount of the secondary loops of the transformer.<\/span><\/p>\n

Known :\"Step-up<\/u><\/span><\/p>\n

Primary voltage (VP<\/sub>) = 220 Volt<\/span><\/p>\n

Primary loops (NP<\/sub>) = 200 loops<\/span><\/p>\n

Secondary voltage (VS<\/sub>) = 1100 Volt<\/span><\/p>\n

Wanted :<\/u> Secondary loops (NS<\/sub>)<\/span><\/p>\n

Solution :<\/u><\/span><\/p>\n

Vs <\/sub>\/ Ns <\/sub>= Vp<\/sub> \/ Np<\/sub><\/span><\/p>\n

1100 Volt \/ Ns <\/sub>= 220 Volt \/ 200 loops<\/span><\/p>\n

1100 \/ Ns <\/sub>= 220 \/ 200<\/span><\/p>\n

1100 \/ Ns <\/sub>= 1.1<\/span><\/p>\n

Ns <\/sub>= 1100 \/ 1.1<\/span><\/p>\n

Ns <\/sub>= 1000 loops<\/span><\/p>\n

7. According to figure below, what is the amount of the secondary loops of the transformer.<\/span><\/p>\n

Known :\"Step-up<\/u><\/span><\/p>\n

Primary voltage (VP<\/sub>) = 220 Volt<\/span><\/p>\n

Primary loops (NP<\/sub>) = 200 loops<\/span><\/p>\n

Secondary voltage (VS<\/sub>) = 1100 Volt<\/span><\/p>\n

Wanted :<\/u> Secondary loops (NS<\/sub>)<\/span><\/p>\n

Solution :<\/u><\/span><\/p>\n

Vs <\/sub>\/ Ns <\/sub>= Vp<\/sub> \/ Np<\/sub><\/span><\/p>\n

1100 \/ NS<\/sub> = 220 \/ 200<\/span><\/p>\n

1100 \/ NS<\/sub> = 22 \/ 20<\/span><\/p>\n

1100 \/ NS<\/sub> = 1.1<\/span><\/p>\n

NS<\/sub> = 1100 \/ 1.1<\/span><\/p>\n

NS<\/sub> = 1000 <\/span><\/p>\n

8. <\/span><\/p>\n\n\n\n\n\n
Transformer<\/span><\/td>\nNp<\/span><\/td>\nNs<\/span><\/td>\nVp<\/span><\/td>\nVs<\/span><\/td>\nIp<\/span><\/td>\nIs<\/span><\/td>\n<\/tr>\n
1<\/span><\/td>\n1000<\/span><\/td>\n<\/td>\n120<\/span><\/td>\n12<\/span><\/td>\n0.4<\/span><\/td>\n2<\/span><\/td>\n<\/tr>\n
2<\/span><\/td>\n80<\/span><\/td>\n8<\/span><\/td>\n20<\/span><\/td>\n2<\/span><\/td>\n<\/td>\n2.5<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Based on the above table, if the efficiency of both transformers is the same, 50%, Determine Ns<\/sub> and Ip<\/sub>.<\/span><\/p>\n

Solution :<\/span><\/p>\n

The equation of transformer’s efficiency :<\/span><\/p>\n

\"Transformers<\/span><\/p>\n

Calculate Ns<\/sub> of the transformer 1 :<\/span><\/p>\n

\"Transformers<\/span><\/p>\n

Calculate Ip<\/sub> of the transformer 2 :<\/span><\/p>\n

\"Transformers<\/span><\/p>\n

9.<\/span><\/p>\n

\"Step-up<\/span><\/p>\n

Based on the above figure, which of the following statements about the figure above is correct.<\/span><\/p>\n

A. Figure 1 is a step-up transformer and figure 2 is a step-down transformer<\/span><\/p>\n

B. Figure 1 is a step-down transformer and figure 2 is a step-up transformer<\/span><\/p>\n

C. Figure 1 and 2 are a step-down transformer<\/span><\/p>\n

D. Figure 1 and 2 are a step-up transformer<\/span><\/p>\n

Solution<\/span><\/p>\n

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.<\/span><\/p>\n

The correct answer is B.<\/span><\/span><\/p>\n

10.<\/span><\/p>\n

\"Step-up<\/span><\/p>\n

If the primary coil has 800 loops, then determine the secondary coil.<\/span><\/p>\n

Known :<\/u><\/span><\/p>\n

Primary loops = Np <\/sub>= 800 loops<\/span><\/p>\n

Primary voltage =VP<\/sub> = 220 Volt<\/span><\/p>\n

Secondary voltage = VS<\/sub> = 55 Volt<\/span><\/p>\n

Wanted :<\/u> Secondary loops (NS<\/sub>)<\/span><\/p>\n

Solution :<\/u><\/span><\/p>\n

Vs <\/sub>\/ Ns <\/sub>= Vp<\/sub> \/ Np<\/sub><\/span><\/p>\n

55 \/ Ns <\/sub>= 220 \/ 800<\/span><\/p>\n

55 \/ Ns <\/sub>= 22 \/ 80<\/span><\/p>\n

NS<\/sub> = (80)(55) \/ 22<\/span><\/p>\n

NS<\/sub> = 4400 \/ 22<\/span><\/p>\n

NS<\/sub> = 200 loops<\/span><\/p>\n

11. <\/span><\/p>\n

\"Step-up<\/span><\/p>\n

The correct statement about transformer P and Q is…<\/span><\/p>\n

A. P is a step-down transformer because of Is<\/sub> < Ip<\/sub><\/span><\/p>\n

B. P is a step-up transformer because of Vp<\/sub> < Vs<\/sub><\/span><\/p>\n

C. Q is a step-up transformer because of Vp<\/sub> > Vs<\/sub><\/span><\/p>\n

D. Q is a step-up transformer because Is<\/sub> > Ip<\/sub><\/span><\/p>\n

Solution<\/span><\/p>\n

P is step-up transformer because primary voltage (Vp<\/sub> = 110 V) < secondary voltage (Vs<\/sub> = 200 V).<\/span><\/p>\n

Q is step-down transformer because primary voltage (Vp<\/sub> = 220 V) > secondary voltage (Vs<\/sub> = 110 V).<\/span><\/p>\n

The correct answer is B.<\/span><\/p>\n

    \n
  1. What is the primary function of a transformer?<\/strong><\/span>\n