Transformer Formula Calculator

\[ V_S = V_P \frac{N_S}{N_P} \]

1. What is the Transformer Formula Calculator?

Definition: This calculator computes the secondary voltage (\(V_S\)) of a transformer, given the primary voltage (\(V_P\)), the number of primary turns (\(N_P\)), and the number of secondary turns (\(N_S\)).

Purpose: It is used in electrical engineering to determine the output voltage of a transformer, essential for designing power supplies, electrical grids, and electronic devices.

2. How Does the Calculator Work?

The calculator uses the transformer voltage ratio formula:

Formula: \[ V_S = V_P \frac{N_S}{N_P} \] where:

\(V_S\): Secondary voltage (V, kV, mV)
\(V_P\): Primary voltage (V, kV, mV)
\(N_S\): Number of secondary turns (unitless)
\(N_P\): Number of primary turns (unitless)

Unit Conversions:

Voltage (Primary and Secondary):
- 1 V = 1 V
- 1 kV = 1000 V
- 1 mV = 0.001 V

Steps:

Enter the primary voltage in V, kV, or mV (default 120 V, step size 0.00001).
Enter the number of primary turns (default 200, step size 1).
Enter the number of secondary turns (default 100, step size 1).
Convert primary voltage to base unit (V).
Validate that the number of turns are positive integers.
Calculate secondary voltage: \(V_S = V_P \frac{N_S}{N_P}\).
Convert the secondary voltage to the selected unit.
Display the result, rounded to 4 decimal places.

3. Importance of Transformer Voltage Calculation

Calculating the secondary voltage of a transformer is crucial for:

Electrical Engineering: Designing transformers to step up or step down voltage for power distribution.
Electronics: Ensuring appropriate voltage levels for circuits in devices like chargers and appliances.
Education: Teaching principles of electromagnetic induction and transformer operation in physics and engineering.

4. Using the Calculator

Examples:

Example 1: Calculate the secondary voltage for \(V_P = 120 \, \text{V}\), \(N_P = 200\), \(N_S = 100\), in V:
- Enter \(V_P = 120 \, \text{V}\), \(N_P = 200\), \(N_S = 100\).
- Secondary voltage: \(V_S = 120 \times \frac{100}{200} = 60 \, \text{V}\).
- Result: \( \text{Secondary Voltage} = 60.0000 \, \text{V} \).
Example 2: Calculate the secondary voltage for \(V_P = 230 \, \text{V}\), \(N_P = 500\), \(N_S = 50\), in mV:
- Enter \(V_P = 230 \, \text{V}\), \(N_P = 500\), \(N_S = 50\).
- Secondary voltage: \(V_S = 230 \times \frac{50}{500} = 23 \, \text{V} = 23000 \, \text{mV}\).
- Result: \( \text{Secondary Voltage} = 23000.0000 \, \text{mV} \).

5. Frequently Asked Questions (FAQ)

Q: What is a transformer?
A: A transformer is an electrical device that transfers electrical energy between two circuits by changing voltage levels through electromagnetic induction.

Q: Why must the number of turns be positive integers?
A: The number of turns represents the number of loops in the transformer coils, which must be positive integers for a physically realistic transformer.

Q: What happens if \(N_S > N_P\)?
A: If \(N_S > N_P\), the transformer steps up the voltage (\(V_S > V_P\)); if \(N_S < N_P\), it steps down the voltage (\(V_S < V_P\)).