# Voltage Transformation Ratio (K)

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 N1 = 400

Secondary turns, N2 = 100

Primary induced voltage,   E1 = V1 = 2000 V

(i) Secondary voltage on open, circuit V2

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 E1 = V1 = 6600 V

Secondary, E2 = V2 = 600V

Maximum value of flux ɸmax = 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 cm2. 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, N1 = 500

Secondary turns, N2 = 100

Primary, E1 = V1 = 230 V

Core area, α = 60 cm2 = 60 × 10-4 m2

(i) Transformation ratio, K:

Hence, K = 0.2. (Ans.)

(ii) Maximum value of flux density, Bmax:

Using the e.m.f. equation, E1 = 4.44fɸmax N1

230 = 4.44 × 50 × ɸmax × 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,             E1 = 3300 V

N1 = 1100

Secondary, E2 = 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, E1 = 220 V

Secondary, E2 = 550 V

Max. flux density, Bmax = 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 m2 ;

Bmax = 1.3 Wb/m2,

f = 50 Hz ;

E1 = 11000 V

E2 = 550 V

Stacking factor = 0.9

(i) Number of turns N1 (h.v.) ; N2 (l.v.)

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

ɸmax = 1.3 × 400 × 10-4 × 0.9 = 0.0468 Wb

E1 = 4.44fɸmax N1

11000 = 4.44 × 50 × 0.0468 × N1