PhysicsSolver360 logoPhysicsSolver360°
Powered by Solver360°

Transformer Calculator

Calculate transformer voltage ratios, current ratios, and efficiency with interactive visualization

Parameters

Vⓘ
Input voltage to primary coil
Vⓘ
Output voltage from secondary coil
ⓘ
Number of turns in primary coil
ⓘ
Number of turns in secondary coil
Aⓘ
Current in primary coil
%ⓘ
Transformer efficiency percentage
Transformer Analysis
Enter values to calculate ratios, currents, and efficiency

Calculated Values

Turns Ratio:
10.0000;10.0000;
Voltage Ratio:
10.0000;10.0000;
Secondary Current:
0.1000;A0.1000;A
Power Loss:
6.0000;W6.0000;W

Examples

Example 1: Step-down Transformer

A 120V to 12V transformer with 1000:100 turns ratio.

  • Turns Ratio: 1010
  • Voltage Ratio: 1010
  • Secondary Current: 1010
  • Power Loss: 66

Example 2: Step-up Transformer

A 12V to 120V transformer with 100:1000 turns ratio.

  • Turns Ratio: 0.10.1
  • Voltage Ratio: 0.10.1
  • Secondary Current: 11
  • Power Loss: 1212

Example 3: Power Transformer

A 240V to 24V transformer with 2000:200 turns ratio.

  • Turns Ratio: 1010
  • Voltage Ratio: 1010
  • Secondary Current: 5050
  • Power Loss: 2424

Transformers and Electromagnetic Induction

A transformer is an electrical device that transfers electrical energy between two or more circuits through electromagnetic induction. It consists of two or more coils of wire wound around a common magnetic core.

The primary coil is connected to the input voltage source, while the secondary coil provides the output voltage. The voltage ratio is determined by the turns ratio: Vp/Vs = Np/Ns, where Vp and Vs are the primary and secondary voltages, and Np and Ns are the number of turns.

According to the principle of conservation of energy, the power input to the primary should equal the power output from the secondary (neglecting losses). This means VpIp = VsIs, where Ip and Is are the primary and secondary currents.

The current ratio is inversely proportional to the voltage ratio: Ip/Is = Ns/Np. This is why step-up transformers (increasing voltage) decrease current, while step-down transformers (decreasing voltage) increase current.

Transformer efficiency is the ratio of output power to input power, expressed as a percentage. Real transformers have losses due to resistance in the windings, hysteresis in the core, and eddy currents.

Key Concepts

  • Voltage Ratio: Vp/Vs = Np/Ns (proportional to turns ratio)
  • Current Ratio: Ip/Is = Ns/Np (inversely proportional to turns ratio)
  • Power Conservation: VpIp = VsIs (ideal transformer)
  • Turns Ratio: Np/Ns (determines voltage transformation)
  • Efficiency: η = (Pout/Pin) × 100% (accounting for losses)
  • Step-up/Step-down: Determined by turns ratio

Real-World Applications

  • Power Distribution: High voltage transmission, low voltage distribution
  • Electronics: Power supplies and voltage regulation
  • Audio Equipment: Impedance matching for speakers
  • Isolation: Electrical isolation between circuits
  • Measurement: Current and voltage measurement transformers

Physics Equations

Voltage Ratio:
VpVs=NpNs\frac{V_p}{V_s} = \frac{N_p}{N_s}
Current Ratio:
IpIs=NsNp\frac{I_p}{I_s} = \frac{N_s}{N_p}
Power Conservation:
VpIp=VsIsV_p I_p = V_s I_s
Turns Ratio:
a=NpNsa = \frac{N_p}{N_s}
Efficiency:
η=PoutPin×100%\eta = \frac{P_{out}}{P_{in}} \times 100\%

Step-by-Step Solution

See how the main results are calculated.

1

Step 1: Identify Known Values

List the given values from the problem:

Equation:

\text{Given: } V_p = ${Vp} \text{ V}, V_s = ${Vs} \text{ V}, N_p = ${Np}, N_s = ${Ns}, I_p = ${Ip} \text{ A}, \eta = ${eff}\%

Calculation:

Vp=120 VVs=12 VNp=1000Ns=100Ip=1 Aη=95%V_p = 120 \text{ V} \\ V_s = 12 \text{ V} \\ N_p = 1000 \\ N_s = 100 \\ I_p = 1 \text{ A} \\ \eta = 95\%

Explanation:

We start by identifying what values we know and what we need to find.

2

Step 2: Calculate Turns Ratio

Use the turns ratio formula:

Equation:

a=NpNsa = \frac{N_p}{N_s}

Calculation:

a=1000100=10.00a = \frac{1000}{100} = 10.00

Explanation:

The turns ratio determines the voltage transformation ratio.

3

Step 3: Calculate Voltage Ratio

Use the voltage ratio formula:

Equation:

VpVs=NpNs\frac{V_p}{V_s} = \frac{N_p}{N_s}

Calculation:

VpVs=12012=10.00\frac{V_p}{V_s} = \frac{120}{12} = 10.00

Explanation:

The voltage ratio should equal the turns ratio in an ideal transformer.

4

Step 4: Calculate Secondary Current

Use the current ratio formula:

Equation:

Is=Ip×NpNsI_s = I_p \times \frac{N_p}{N_s}

Calculation:

Is=1×1000100=0.10 AI_s = 1 \times \frac{1000}{100} = 0.10 \text{ A}

Explanation:

The current ratio is inversely proportional to the turns ratio.

5

Step 5: Calculate Power Loss

Use the efficiency formula:

Equation:

Ploss=Pin−Pout=Pin×(1−η100)P_{loss} = P_{in} - P_{out} = P_{in} \times (1 - \frac{\eta}{100})

Calculation:

Ploss=120.00×(1−95100)=6.00 WP_{loss} = 120.00 \times (1 - \frac{95}{100}) = 6.00 \text{ W}

Explanation:

Power loss is the difference between input and output power due to inefficiency.

Frequently Asked Questions (FAQ)

What is a transformer?

A transformer is an electrical device that transfers electrical energy between circuits through electromagnetic induction. It can step up or step down voltage while maintaining power conservation.

How do I calculate the voltage ratio?

The voltage ratio is calculated as Vp/Vs = Np/Ns, where Vp and Vs are the primary and secondary voltages, and Np and Ns are the number of turns in each coil.

What is the relationship between voltage and current in a transformer?

In an ideal transformer, the current ratio is inversely proportional to the voltage ratio: Ip/Is = Ns/Np. Step-up transformers increase voltage but decrease current.

What is transformer efficiency?

Transformer efficiency is the ratio of output power to input power, expressed as a percentage. Real transformers have losses due to resistance, hysteresis, and eddy currents.

What is the difference between step-up and step-down transformers?

Step-up transformers increase voltage (Np < Ns), while step-down transformers decrease voltage (Np > Ns). The current changes in the opposite direction to maintain power conservation.

Why do transformers have losses?

Transformers have losses due to resistance in the windings (copper losses), hysteresis in the magnetic core, and eddy currents. These losses reduce the efficiency below 100%.

Practice MCQs

  1. If the turns ratio is 2:1, the voltage ratio is:
  2. A step-up transformer:
  3. What is the secondary current if primary current is 2A and turns ratio is 10:1?
  4. Transformer efficiency is maximum when:
  5. Which of the following is NOT a transformer loss?