Induced Voltage Formula

Electromagnetic induction is the phenomenon in which a conductor is placed in a certain position and the magnetic field varies or remains stationary as the conductor moves. As a result, this produces a voltage or electromotive force across the electrical conductor known as the induced voltage. The concept of induced voltage is explained by Faraday’s law of induction. The law states that the induced voltage is defined as the rate of change of magnetic flux with respect to the time via a closed circuit.

What is Induced Voltage?

Electromagnetic induction plays an integral role in the generation of the induced voltage. The induced voltage is directly proportional to the number of turns in the coil, magnetic field, and cross-section of the loop while it changes inversely with an increase in time. 

• It is denoted by the symbol ε. 
• Its unit of measurement is volts (V) and the dimensional formula is given by [M¹L²A⁻¹T⁻³].

Induced Voltage Formula 

The formula to calculate the induced voltage is,

ε = N × dΦ/dt

where,

• ε is the induced voltage,
• N is the number of turns in the coil,
• dΦ is the magnetic flux,
• dt is the time taken.

The above formula is also termed as the relation between induced voltage and the magnetic flux. 

Now, in terms of the magnetic field across the conductor and its area, the formula for induced voltage is expressed as:

ε = NBA/t

where,

• ε is the induced voltage,
• N is the number of turns in the coil,
• B is the magnetic field,
• A is the area of coil,
• t is the time taken.

Sample Problems

Problem 1: Calculate the induced voltage of a coil of 10 turns if flux is 2 Tm² for 5 s.

Solution:

We have,

N = 10

dΦ = 2

dt = 5

Using the formula we have,

ε = N × dΦ/dt

= 10 × 2/5

= 4 V

Problem 2: Calculate the induced voltage of a coil of 5 turns if flux is 2.5 Tm² for 3 s.

Solution:

We have,

N = 5

dΦ = 2.5

dt = 3

Using the formula we have,

ε = N × dΦ/dt

= 10 × 2.5/3

= 25/3

= 8.33 V

Problem 3: Calculate the induced voltage of a coil of 12 turns if flux is 5 Tm² for 10 s.

Solution:

We have,

N = 12

Φ = 5

t = 10

Using the formula we have,

ε = N × dΦ/dt

= 12 × 5/10

= 6 V

Problem 4: Calculate the flux if the induced voltage of a coil of 7 turns is 9 V for 8 s.

Solution:

We have,

ε = 9

N = 7

dt = 8

Using the formula we have,

ε = N × dΦ/dt

dΦ = ε dt/N

= 9 (8/7)

= 10.28 Tm²

Problem 5: Calculate the flux if the induced voltage of a coil of 12 turns is 7 V for 10 s.

Solution:

We have,

ε = 7

N = 12

dt = 10

Using the formula we have,

ε = N × dΦ/dt

=> dΦ = ε dt/N

= 7 (10/12)

= 5.83 Tm²

Problem 6: Calculate the number of turns if flux is 2.93 Tm², the induced voltage is 11 V for 4 s.

Solution:

We have,

ε = 11

dΦ = 2.93

dt = 4

Using the formula we have,

ε = N × dΦ/dt

or

N = ε dΦ/dt

= 11 (2.93/4)

= 8 turns.

Problem 7: Calculate the induced voltage for the number of turns as 7, magnetic field as 12 T, cross-section area 10 sq. m, and time of 5 s. 

Solution:

We have,

B = 12

A = 10

N = 7

dt = 5

Calculate the magnetic flux.

dΦ = BA

= 12 (10)

= 120 Tm²

Using the formula we have,

ε = N × dΦ/dt

= 7 (120/5)

= 168 V