Transformer Formula (Class 12 Physics)
The Transformer Formula is a core concept in Class 12 Physics (Alternating Current). It defines the relationship between the voltage, current, and the number of turns in the primary and secondary coils of a transformer. Mastering these formulas is essential for solving numericals in CBSE board exams, JEE, and NEET.
Class: 12
Topic: Alternating Current (AC)
Exams: CBSE · JEE · NEET
What is a Transformer?
A transformer is a passive electrical device that transfers electrical energy from one alternating-current (AC) circuit to one or more other circuits. It operates on the principle of mutual induction.
Transformers are used to either increase (step-up) or decrease (step-down) voltage levels while keeping the frequency constant.
[Image of a transformer circuit diagram showing primary and secondary coils]
1. Transformer Voltage & Turns Ratio Formula
The most fundamental transformer equation relates the voltage across the coils to the number of turns (windings) in each coil. The voltage is directly proportional to the number of turns.
Transformer Turns Ratio Formula
VsVp = NsNp
- Vs = Voltage across the secondary coil
- Vp = Voltage across the primary coil
- Ns = Number of turns in the secondary coil
- Np = Number of turns in the primary coil
Note: The ratio (Ns / Np) is often denoted by the letter 'k' and is called the Transformation Ratio.
2. Transformer Current Formula
In an ideal transformer, there is no power loss. This means the power input to the primary coil equals the power output from the secondary coil (Pin = Pout). Since Power = Voltage × Current (P = VI), current is inversely proportional to voltage and turns.
Transformer Current Formula
IpIs = VsVp = NsNp
- Ip = Current in the primary coil
- Is = Current in the secondary coil
This means if a transformer steps up the voltage, it must step down the current to conserve energy.
3. Transformer Efficiency Formula
In real-world applications, transformers experience energy losses (due to copper loss, eddy currents, hysteresis, etc.). The efficiency (η) indicates how well the transformer converts input power into useful output power.
Transformer Efficiency (η)
η = Output PowerInput Power × 100
η = Vs × IsVp × Ip × 100
An ideal transformer has 100% efficiency, but practical transformers usually operate between 90% and 99% efficiency.
4. Step-Up vs. Step-Down Transformers
Based on the turns ratio (k = Ns / Np), transformers are classified into two main types:
Step-Up Transformer: Ns > NpIncreases voltage (Vs > Vp) and decreases current (Is < Ip). Transformation ratio k > 1.
Step-Down Transformer: Ns < NpDecreases voltage (Vs < Vp) and increases current (Is > Ip). Transformation ratio k < 1.
Master Table of Transformer Formulas
| Formula Type |
Mathematical Expression |
Condition |
| Voltage & Turns Ratio |
Vs / Vp = Ns / Np |
Valid for all transformers |
| Current Ratio |
Ip / Is = Vs / Vp = Ns / Np |
For 100% ideal transformers |
| Efficiency (η) |
η = (Pout / Pin) × 100 |
Used for practical/real transformers |
Solved Examples on Transformer Formula
Example 1: Calculating Secondary Voltage
A transformer has 500 turns in its primary coil and 2000 turns in its secondary coil. If the primary voltage is 220V, what is the secondary voltage?
Given: N
p = 500, N
s = 2000, V
p = 220V
Formula: V
s / V
p = N
s / N
p
Vs / 220 = 2000 / 500
Vs / 220 = 4
Vs = 220 × 4 = 880V
Answer: Secondary Voltage (Vs) = 880V (It is a step-up transformer)
Example 2: Calculating Primary Current
An ideal step-down transformer reduces 4400V to 220V. If the secondary coil draws a current of 10A, find the primary current.
Given: V
p = 4400V, V
s = 220V, I
s = 10A
Formula: I
p / I
s = V
s / V
p
Ip / 10 = 220 / 4400
Ip / 10 = 1 / 20
Ip = 10 / 20 = 0.5A
Answer: Primary Current (Ip) = 0.5A
Example 3: Transformer Efficiency Calculation
A transformer operates on a 200V mains and draws 5A of primary current. The secondary coil outputs 100V and 8A. Calculate the efficiency of the transformer.
Given: V
p = 200V, I
p = 5A, V
s = 100V, I
s = 8A
Input Power (Pin) = V
p × I
p = 200 × 5 = 1000W
Output Power (Pout) = V
s × I
s = 100 × 8 = 800W
Formula: η = (Pout / Pin) × 100
η = (800 / 1000) × 100 = 0.8 × 100 = 80%
Answer: Efficiency = 80%
Top Queries Answered (FAQs)
What is the transformer formula?
The main transformer formula relates voltage to the number of turns: Vs / Vp = Ns / Np. It dictates that the voltage ratio is exactly equal to the turns ratio between the secondary and primary coils.
How do you calculate transformer efficiency?
Transformer efficiency is calculated using the formula: η = (Output Power / Input Power) × 100. You can expand this to η = [(Vs × Is) / (Vp × Ip)] × 100.
What is the formula for a step-up transformer?
The formula remains the same (Vs / Vp = Ns / Np), but for a step-up transformer, the condition is always Ns > Np, which results in Vs > Vp.
Why is current inversely proportional to voltage in a transformer?
According to the law of conservation of energy, an ideal transformer cannot create power. Since Power = Voltage × Current (P=VI), if voltage goes up (step-up), the current must go down to keep the overall power constant.