Question

What is meant by the transformation ratio of a transformer? In a step-down transformer, the transmission line voltage of 2200 volt is changed to 220 volt. Number of turns in the primary coil is 5000. The efficiency of the transformer is 90 percent and output power is 8kW.

Hint:

The efficiency of a transformer is always less than 100\% due to energy losses such as eddy currents and hysteresis in the core.

Answer 1

Transformation Ratio (\( k \)):

The transformation ratio of a transformer is the ratio of the secondary voltage (\( V_s \)) to the primary voltage (\( V_p \)). It is given by the formula:

\[ k = \frac{V_s}{V_p} = \frac{N_s}{N_p} \]

Given Data:

\[ V_p = 2200 \text{ V} \quad \text{(Primary voltage)} \] \[ V_s = 220 \text{ V} \quad \text{(Secondary voltage)} \] \[ N_p = 5000 \quad \text{(Turns in the primary coil)} \] \[ \eta = 90\% = 0.90 \quad \text{(Efficiency)} \] \[ P_{\text{out}} = 8 \text{ kW} = 8000 \text{ W} \quad \text{(Output power)} \]

(i) Calculation of Transformation Ratio (\( k \)):

\[ k = \frac{V_s}{V_p} = \frac{220}{2200} = 0.1 \]

(ii) Calculation of Number of Turns in the Secondary Coil (\( N_s \)):

Using the turns ratio formula: \[ \frac{N_s}{N_p} = \frac{V_s}{V_p} \] \[ N_s = N_p \times \frac{V_s}{V_p} = 5000 \times \frac{220}{2200} \] \[ N_s = 500 \quad \text{(Turns in secondary coil)} \]

(iii) Calculation of Input Power (\( P_{\text{in}} \)):

The efficiency of a transformer is given by: \[ \eta = \frac{P_{\text{out}}}{P_{\text{in}}} \] \[ P_{\text{in}} = \frac{P_{\text{out}}}{\eta} = \frac{8000}{0.90} \] \[ P_{\text{in}} = 8888.89 \text{ W} \approx 8.89 \text{ kW} \]

Final Answers:

• (i) Transformation ratio (\( k \)) = \( 0.1 \)
• (ii) Number of turns in the secondary coil (\( N_s \)) = \( 500 \)
• (iii) Input power (\( P_{\text{in}} \)) = \( 8.89 \) kW