Chapter 15 Electromagnetism (Numerical Problems)
15.1. A transformer is needed to convert a mains 240 V supply into a 12 V supply. If there are 2000 turns on the primary coil, then find the number of turns on the secondary coil.ย ย
15.2. A step-up transformer has a turn ratios of 1 : 100. An alternating supply of 20 V is connected across the primary coil. What is the secondary voltage?ย
15.3. A step-down transformer has a turns ratio of 100 : 1. An ac voltage of amplitude 170 V is applied to the primary. If the current in the primary is 1.0 mA, what is the current in the secondary?ย ย
15.4. A transformer, designed to convert the voltage from 240 V A.C mains to 12 V, has 4000 turns on the primary coil. How many turns should be on the secondary coil? If the transformer were 100% efficient, what current would flow through the primary coil when the current in the secondary coil was 0.4 A?
15.5. A power station generates 500 MW of electrical power which is fed to a transmission line. What current would flow in the transmission line, if the input voltage is 250 kV?
15.1. A transformer is needed to convert a mains 240 V supply into a 12 V supply. If there are 2000 turns on the primary coil, then find the number of turns on the secondary coil.ย ย
Solution: Given data
Voltage across primary Vp = 240 Volts
Voltage across secondary Vs = 12 volts
Number of turns of primary coil Np = 200
Number of turns of secondary coil Ns = ?
Formula Ns / Np = Vs / Vp
putting values we get Ns = (Vs / Vp ) x Np
Ns = (12/240) x 200
Ns = 100
So, there are 100 turns in the secondary coil.
15.2. A step-up transformer has a turn ratios of 1 : 100. An alternating supply of 20 V is connected across the primary coil. What is the secondary voltage?ย
Solution: Given data
We have step up transformer
Turn ratio is 1:100 It mean Np:Ns = 1:100
โย ย Np / Ns = 1/100
Voltage across primary Vp = 20 Volts
Voltage across secondary Vs = ?
Formula: Vs / Vp = Ns/Np
Putting the values we get
Vs = 100 x 20
Vs = 2000 Volts
Hence 2000 volts will be produced across the secondary coil.
15.3. A step-down transformer has a turns ratio of 100 : 1. An ac voltage of amplitude 170 V is applied to the primary. If the current in the primary is 1.0 mA, what is the current in the secondary?ย ย
Solution: Given data
We have step down transformer
Turn ratio is 1:100 It mean Ns : Np = 1 : 100
Ns / Np = 1/100
Voltage across primary Vp = 170 Volts
Current across primary Ip = 1.0 mA = 1.0 x 10-3 ampere
Current across secondary Is = ?
Formula: Vs / Vp = Ns/Np
Putting the values we get
Vs / Vp = 1 /100
We know that P = IV and by law of conservation of energy.
Output Power = Input Power
Is Vs = IpVp
Is = Ip x Vp / Vs
Is = 1.0 x 10-3 x 100
Is = 0.1 Ampere
Hence 0.1 Ampere current will flow in the secondary coil.
15.4. A transformer, designed to convert the voltage from 240 V a.c mains to 12 V, has 4000 turns on the primary coil. How many turns should be on the secondary coil? If the transformer were 100% efficient, what current would flow through the primary coil when the current in the secondary coil was 0.4 A?
Solution: Given data
We have step down transformer
Voltage across primary Vp = 240 Volts
Voltage across secondary Vs = 12 Volts
Number of turns of primary coil Np = 4000
Number of turns of secondary coil Ns = ?
The transformer is 100 % it means Output power = Input power
IsVs = IpVp
Current across secondary coil Is = 0.4 Ampere
Current across primary Ip = ?
Formula: Ns / Np = Vs / Vp
Ns = (12/240) x 400
Ns = 200
We know P = IV and by law of conservation of energy
Input power = Output power
IpVp = IsVs
Therefore Ip = Is x Vs / Vp
putting value we get
Ip = 0.4 x (12/240)
Ip = 0.02 Ampere
Hence, 0.02 Ampere current will flow in the primary coil.
15.5. A power station generates 500 MW of electrical power which is fed to a transmission line. What current would flow in the transmission line, if the input voltage is 250 kV?
Solution: Given data
Power generated P = 500MW = 500 x 106 watt
โด 1M = 106
Input voltage Vin = 250 kV = 250 x 103 volts
Current I = ?
We know power P = IV
We can write Pin = Iin Vin
Iin = Pin / Vin
Putting the values we get
Iin = (500 x 106 ) / (250 x 103 )
Iin = 2.0 x 103 A
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