Explain the concept of EMI with regards to a step up transformer

Key Concepts to Know

1. Faraday’s Law of EMI
   The induced electromotive force (EMF) in a coil is proportional to the rate of change of magnetic flux through it:

   $\left|\mathcal{E}\right| = N\,\left|\frac{d\Phi_B}{dt}\right|$

   where $N$ is number of turns and $\Phi_B$ is magnetic flux.

2. AC Source in Primary Coil
   An alternating current produces a time-varying magnetic field in the iron core. Because the field changes continuously, $\frac{d\Phi_B}{dt}$ is never zero → continuous EMF in the secondary.

3. Transformer Equations
   For an ideal transformer (no losses):

   $\frac{V_s}{V_p} = \frac{N_s}{N_p}$ $\frac{I_s}{I_p} = \frac{N_p}{N_s}$

   $V$ = voltage, $I$ = current, subscripts $p$ (primary) and $s$ (secondary).

4. Step-Up Condition
   In a step-up transformer, $N_s > N_p$ so $V_s > V_p$. The secondary voltage is higher, but current is proportionally lower (power ideally conserved).

Logical Chain a Student Follows

1. Realise a transformer needs AC, not DC, because EMI depends on changing flux.
2. Apply Faraday’s Law separately to primary and secondary.
3. Use perfect magnetic coupling assumption (same flux through both coils) to equate flux.
4. Divide the EMFs to get the turns ratio relation.
5. Conclude when $N_s$ is greater, voltage steps up. Energy conservation tells you current must step down.

Imagine You Have Two Coils and a Moving Magnet

1. Magnet Trick: When you move a magnet near a coil, electricity appears in the coil. This magic is called Electromagnetic Induction (EMI).
2. Transformer Toy: A transformer is like two coils (primary and secondary) sitting next to each other on an iron core. You never move a magnet; instead you send AC current in the first coil. That AC current behaves like a moving magnet.
3. Step-Up Idea: If the second coil has more turns (loops) than the first, the electricity (voltage) in the second coil gets bigger. So it "steps up" the voltage. Think of winding a long spring versus a short spring: the longer one stretches (voltage) more!

So EMI in a step-up transformer means: AC current in primary → changing magnetic field → induces bigger voltage in secondary because it has more turns.

Deriving the Step-Up Relation Using EMI

1. Flux Linkage
   Let the instantaneous magnetic flux in the core be $\Phi(t)$.
2. EMF in Primary
   $\mathcal{E}_p = -N_p\,\frac{d\Phi}{dt}$ For an ideal transformer (ignoring resistance), $\mathcal{E}_p$ equals the applied primary voltage $V_p$ (phasor sense).
3. EMF in Secondary
   $\mathcal{E}_s = -N_s\,\frac{d\Phi}{dt}$ This is the induced secondary voltage $V_s$.
4. Divide the Two Equations
   $\frac{V_s}{V_p} = \frac{N_s}{N_p}$
5. Step-Up Condition
   If $N_s > N_p$ then $V_s > V_p$ so the transformer is step-up.
6. Current Relation (for completeness)
   Assuming no loss, $V_p I_p = V_s I_s \implies \frac{I_s}{I_p} = \frac{N_p}{N_s}$

Final Result: A step-up transformer uses EMI to raise voltage according to the turns ratio $N_s:N_p$; power remains (ideally) the same while current decreases.