The turns ratio is a fundamental concept in the realm of transformers. It defines the relationship between the number of turns in the primary winding and the number of turns in the secondary winding. This ratio is vital because it determines how a transformer will modify the input voltage and current.
Definition:
The turns ratio (often denoted as (N)) of a transformer is given by:
[N = \frac{N_p}{N_s}]
Where:
- (N_p) = Number of turns on the primary winding
- (N_s) = Number of turns on the secondary winding
Voltage and Turns Ratio:
The relationship between the primary and secondary voltages and the turns ratio is:
[ \frac{V_p}{V_s} = \frac{N_p}{N_s} ]
Where:
- (V_p) = Voltage on the primary winding
- (V_s) = Voltage on the secondary winding
Current and Turns Ratio:
Because of the conservation of energy, the power in the primary coil must equal the power in the secondary coil (ignoring losses). Therefore:
[ V_p \times I_p = V_s \times I_s ]
Given the voltage relationship, this also implies:
[ \frac{I_p}{I_s} = \frac{N_s}{N_p} ]
Where:
- (I_p) = Current in the primary winding
- (I_s) = Current in the secondary winding
Applications:
- Step-Up Transformers: If the secondary winding has more turns than the primary winding ((N_p < N_s)), the transformer will increase the voltage from the primary to the secondary, making it a step-up transformer.
- Step-Down Transformers: Conversely, if the primary winding has more turns than the secondary ((N_p > N_s)), the transformer will decrease the voltage, making it a step-down transformer.
Example:
Suppose a transformer has a turns ratio of 10:1 (primary to secondary). If the primary voltage is 220V, the secondary voltage will be 22V.
In practice, when designing or analyzing transformers, understanding the turns ratio is crucial since it directly impacts the voltage and current transformation properties of the device.