Question

The primary winding of a single-phase iron core transformer is connected to a 74 V, 50 Hz source. The primary and secondary windings have 100 and 400 turns respectively. If 25% of the flux in the primary winding leaks into the air, the mutual flux in the core will have a peak value of
1. 0.25 mWb
2. 0.5 mWb
3. 2.5 mWb
4. 5 mWb

Answer 1

Correct Answer - Option 3 : 2.5 mWb

Emf equation of Transformer:

RMS value of induced EMF in the primary winding (E1) = 4.44 f N1 ϕm

RMS value of induced EMF in the secondary winding (E2) = 4.44 f N2 ϕm

Where N1 = number of turns in the primary winding

N2 = number of turns in the secondary winding

ϕm = Maximum or peak value of flux in the core (in Wb) 

f = frequency of the AC supply (in Hz)

Calculation:

Given that,

Primary voltage (E₁) = 75 V

Frequency f = 50 Hz

N₁ = 100, N₂ = 400

25% of the flux in the primary winding is leaked into the air, which means only 75% of primary flux is linking with the secondary.

⇒ (E1) = 4.44 f N1 ϕ_m1 = 74 V

⇒ 74 = 4.44 × 50 × 100 × ϕ_m1

⇒ ϕ_m1 = 3.333 mW

As only 75% primary flux links with secondary, the secondary flux or mutual flux in the core is given by

ϕ_m2 = 0.75 ϕ_m1

⇒ ϕ_m2 = 0.75 × 3.3333 = 2.5 mW

∴ The mutual flux in the core will have a peak value of 2.5 mW