Recall and use the equation for 100% efficiency in a transformer I_p V_p = I_s V_s where p and s refer to primary and secondary

4.5.6 The Transformer

Objective

Recall and use the equation for a transformer that is assumed to be 100 % efficient:

\$Ip Vp = Is Vs\$

where the subscripts p and s refer to the primary and secondary windings respectively.

1. What is a Transformer?

A transformer is a static electrical device that transfers electrical energy between two or more circuits through electromagnetic induction. It consists of:

• A laminated iron core.
• A primary winding (input).
• A secondary winding (output).

2. Principle of Operation

When an alternating current (AC) flows through the primary winding, it creates a time‑varying magnetic flux \$\Phi\$ in the core. This changing flux links the secondary winding and induces an emf according to Faraday’s law:

\$\mathcal{E}p = -Np \frac{d\Phi}{dt}, \qquad \mathcal{E}s = -Ns \frac{d\Phi}{dt}\$

Because the same flux \$\Phi\$ links both windings, the ratio of the induced emfs equals the ratio of the number of turns:

\$\frac{Vs}{Vp} = \frac{Ns}{Np}\$

3. Ideal (100 % Efficient) Transformer

In an ideal transformer:

• No energy is lost as heat, sound, or stray magnetic fields.
• All input power equals output power.

Therefore:

\$P{\text{in}} = P{\text{out}} \quad\Longrightarrow\quad Ip Vp = Is Vs\$

This is the equation we must be able to recall and apply.

4. Relationship Between Turns, Voltage and Current

5. Using the Equation \$Ip Vp = Is Vs\$

1. Identify which quantities are given (usually two of the four: \$Ip\$, \$Vp\$, \$Is\$, \$Vs\$).
2. Substitute the known values into the equation.
3. Solve for the unknown quantity.
4. If the problem also provides the turns ratio, you may first find the missing voltage or current using the turns‑ratio relationships, then apply the power equation for verification.

6. Example Problem

Question: A step‑down transformer has 500 turns on the primary and 100 turns on the secondary. The primary is connected to a 240 V, 50 Hz supply and draws a current of 2 A. Assuming 100 % efficiency, find the secondary voltage and current.

Solution:

1. Calculate the turns ratio: \$\frac{Np}{Ns}= \frac{500}{100}=5\$
2. Voltage ratio (step‑down): \$\frac{Vs}{Vp}= \frac{Ns}{Np}= \frac{1}{5}\$
3. Secondary voltage: \$Vs = Vp \times \frac{1}{5}= 240\;\text{V} \times 0.2 = 48\;\text{V}\$
4. Apply the power equation: \$Ip Vp = Is Vs\$
5. Solve for \$Is\$: \$Is = \frac{Ip Vp}{V_s}= \frac{2\;\text{A}\times240\;\text{V}}{48\;\text{V}} = 10\;\text{A}\$

Therefore, the secondary delivers 48 V at 10 A.

7. Common Mistakes to Avoid

• Confusing the direction of the turns ratio – remember that a step‑up transformer has \$Ns > Np\$, a step‑down has \$Ns < Np\$.
• Using the power equation without confirming that the transformer can be treated as ideal. Real transformers have losses; for IGCSE questions they are usually ignored.
• Mixing up primary and secondary symbols; keep \$p\$ for primary, \$s\$ for secondary consistently.

8. Practice Questions

1. A transformer has 250 turns on the primary and 500 turns on the secondary. The primary is connected to a 120 V source and draws 0.8 A. Assuming 100 % efficiency, calculate the secondary voltage and current.
2. A step‑down transformer reduces 240 V to 30 V. If the secondary supplies a lamp that draws 3 A, what is the primary current?
3. In an ideal transformer, the primary voltage is 230 V and the secondary voltage is 115 V. If the secondary current is 4 A, find the primary current.

9. Summary

• For an ideal transformer, input power equals output power: \$Ip Vp = Is Vs\$.
• The turns ratio links voltage and current ratios: \$\displaystyle\frac{Np}{Ns}= \frac{Vp}{Vs}= \frac{Is}{Ip}\$.
• Use the power equation to find any missing quantity when two of the four variables are known.
• Remember that real transformers are not 100 % efficient, but the IGCSE syllabus treats them as ideal unless otherwise stated.