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.  
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? 
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?  
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.  

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? 

Solution: Given data

We have step up transformer

Turn ratio is 1:100 It mean Np:Ns = 1:100

⇒   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?  

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

∴ 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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