Transformers

A transformer is an electrical device that transfers electrical energy between two or more circuits through electromagnetic induction. It consists of primary and secondary windings wrapped around a magnetic core. The primary winding is connected to the input voltage, and the secondary winding delivers the output voltage.

Basic Transformer Formulas

The operation of a transformer can be described using several key formulas:

Turns Ratio: N_p / N_s = V_p / V_s (where N = number of turns, V = voltage)
Voltage Ratio: V_s = V_p × (N_s / N_p)
Current Ratio: I_p / I_s = N_s / N_p (where I = current)
Power: P_in = P_out (assuming an ideal transformer with no losses)

Turns Ratio Calculation

The turns ratio of a transformer is the ratio of the number of turns in the primary winding to the number of turns in the secondary winding. It can be calculated using the primary and secondary voltages.

Formula: Np / Ns = Vp / Vs

Formula Breakdown:

Np: Number of primary turns
Ns: Number of secondary turns
Vp: Primary voltage (volts, V)
Vs: Secondary voltage (volts, V)

Example Calculation:

Task: Calculate the turns ratio of a transformer with a primary voltage of 240 volts (V) and a secondary voltage of 24 volts (V).
Solution: Use the turns ratio formula: Np / Ns = Vp / Vs.
Turns Ratio = 240V / 24V = 10:1

Voltage Transformation

Transformers are used to change voltage levels in power distribution systems. The voltage transformation depends on the turns ratio of the transformer windings.

Formula: Vs = Vp × (Ns / Np)

Formula Breakdown:

Vs: Secondary voltage (volts, V)
Vp: Primary voltage (volts, V)
Ns: Number of secondary turns
Np: Number of primary turns

Example Calculation:

Task: Calculate the secondary voltage of a transformer with a primary voltage of 240 volts (V) and a turns ratio of 10:1 (primary:secondary).
Solution: Use the voltage ratio formula: Vs = Vp × (Ns / Np).
Vs = 240V × (1 / 10) = 24V

Current Transformation

Transformers also change the current levels based on the turns ratio. The current in the primary winding is related to the current in the secondary winding.

Formula: Ip / Is = Ns / Np

Formula Breakdown:

Ip: Primary current (amperes, A)
Is: Secondary current (amperes, A)
Ns: Number of secondary turns
Np: Number of primary turns

Example Calculation:

Task: Calculate the primary current of a transformer with a secondary current of 5 amperes (A) and a turns ratio of 1:5 (primary:secondary).
Solution: Use the current ratio formula: Ip / Is = Ns / Np.
Ip = Is × (Np / Ns) = 5A × (1 / 5) = 1A

Power Calculation

In an ideal transformer, the power in the primary winding equals the power in the secondary winding. This means the product of voltage and current remains constant.

Formula: Pin = Pout

Formula Breakdown:

Pin: Primary power (watts, W)
Pout: Secondary power (watts, W)
Vp: Primary voltage (volts, V)
Ip: Primary current (amperes, A)
Vs: Secondary voltage (volts, V)
Is: Secondary current (amperes, A)

Example Calculation:

Task: Verify the power transfer in a transformer with a primary voltage of 120 volts (V), primary current of 2 amperes (A), secondary voltage of 24 volts (V), and secondary current of 10 amperes (A).
Solution: Calculate the primary and secondary power: Pprimary = Vp × Ip and Psecondary = Vs × Is.
Pprimary = 120V × 2A = 240W and Psecondary = 24V × 10A = 240W