The *transformation ratio is defined as the ratio of the secondary voltage to primary voltage. *It is denoted by the letter *K. *

**Example 1**. *A 40 kVA, single phase transformer has 400 turns on the primary and 100 turns **on the **secondary, The primary is connected to 2000 V, 50 Hz supply. Determine: *

*i. **The secondary voltage on open circuit.*

*ii. **The current flowing through the two windings on full-load.*

*iii. **The maximum value of flux.*

**Solution**. Rating = 40 kVA

Primary turns N_{1} = 400

Secondary turns, N_{2} = 100

Primary induced voltage, E_{1} = V_{1} = 2000 V

(i) **Secondary voltage on open, circuit V**_{2}**: **

**Example 2***. **The no-load ratio required in *a *single-phase 50 Hz transformer is 6600/600 V. If the maximum value of flux in the core is to be about 0.08 Wb, find the number of turns in each winding.*

**Solution. **Primary E_{1} = V_{1} = 6600 V

Secondary, E_{2} = V_{2} = 600V

Maximum value of flux ɸ_{max} = 0.08 Wb.

**Example 3**. *A single-phase transformer is connected to a 230 V, *50 *Hz supply. The net cross-sectional area of the core is *60 *cm ^{2}. The number of turns in the primary is 500 and in the secondary 100. Determine: *

*(i) **Transformation ratio. *

*(ii) **E.m.f. induced in secondary winding. *

*(iii) **Maximum value of flux density in the core.*

**Solution**. Primary turns, N_{1} = 500

Secondary turns, N_{2} = 100

Primary, E_{1} = V_{1} = 230 V

Core area, α = 60 cm^{2} = 60 × 10^{-4} m^{2}

(i) **Transformation ratio, ****K: **

Hence, **K ****= ****0.2. (Ans.)**

(ii) **Maximum value of flux density, ****B _{max}: **

Using the e.m.f. equation, E1 = 4.44fɸ_{max} N_{1}

230 = 4.44 × 50 × ɸ_{max} × 500

**Example 4**. *3300/300 V single-phase 300 k VA transformer has 1100 primary turns. **Find:*

* i. **Transformation ratio.*

* ii. **Secondary turns.*

* iii. **Voltage */ *turn.*

* iv. **Secondary current when it supplies a load of 200 k *W *at 0.8 power factor lagging.*

**Solution**, Primary, E_{1} = 3300 V

N_{1} = 1100

Secondary, E_{2} = 300 V

Rating of the transformer = 300 kVA

Output = 200 kW

**Example 5**. *The voltage per turn of a single-phase transformer is **1.1 V. When the primary **winding is connected **to **a 220 V, 50 Hz A.C. supply, the secondary voltage is found to be 550 V. Find: *

*(i) **Primary and secondary turns. *

*(ii) **Core **area if the maximum flux density is **1.1 T.*

**Solution**. Voltage per turn = 1.1 V

Primary, E_{1} = 220 V

Secondary, E_{2} = 550 V

Max. flux density, B_{max} = 1.1 T

**Example 6**, *The core of 1000 kVA, 11000/550 V, 50 Hz, single-phase transformer has a cross-section of 20 cm × 20 cm. If the maximum core density is not to exceed 1.3 tesla, calculate:*

*(i) **The number of h.v. and l.v. turns per phase.*

*(ii) **The e.m.f. per turns.*

*Assume a stacking factor of 0.9.*

**Solution. **Given:

A = 20 cm × 20 cm = 400 × 10^{-4} m^{2} ;

B_{max} = 1.3 Wb/m^{2},

f = 50 Hz ;

E_{1} = 11000 V

E_{2} = 550 V

Stacking factor = 0.9

(i) **Number of turns N _{1} (h.v.) ; N_{2} (l.v.)**

We know that, Flux = flux density × area of cross-section × stacking factor

ɸ_{max} = 1.3 × 400 × 10^{-4} × 0.9 = 0.0468 Wb

E_{1} = 4.44fɸ_{max} N_{1}

11000 = 4.44 × 50 × 0.0468 × N_{1}

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