Q.In a transformer, the number of turns in the primary and the secondary are 410 and 1230 respectively. If the current in primary is 6 A, then that in the secondary coil is :

What the Turns Ratio Really Means

Imagine you have two coils of wire wrapped around a shared iron core. One coil (the primary) has a certain number of loops — say 100 turns. The other (the secondary) has a different number — say 200 turns. When you feed AC voltage into the primary, it creates a changing magnetic field that cuts through both coils. That field induces a voltage in the secondary.

The key insight: each turn of wire gets the same "share" of the magnetic push. If one turn in the primary gets 1 volt induced across it, then every turn in the secondary also gets 1 volt. So if the secondary has twice as many turns, it gets twice the total voltage.

That's the whole idea in a nutshell. The turns ratio directly determines how voltage transforms from primary to secondary.

The Precise Relation

The voltage across each coil is proportional to the number of turns:

Where $V_p$ and $V_s$ are the primary and secondary voltages, and $N_p$ and $N_s$ are the number of turns on each coil.

The current relation follows from conservation of energy. An ideal transformer doesn't create or destroy power — it just transforms it. So the power in equals the power out:

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

What This Tells You

If $N_s > N_p$, you have a step-up transformer — secondary voltage is higher, secondary current is lower. If $N_s < N_p$, it's a step-down transformer — secondary voltage is lower, secondary current is higher.

The turns ratio itself is often written as $a = \frac{N_p}{N_s}$ (primary over secondary). Then:

A Concrete Example

A transformer has 500 turns on the primary and 100 turns on the secondary. The primary is connected to 230 V AC.

Turns ratio $a = \frac{500}{100} = 5$. This is a step-down transformer.

Secondary voltage: $V_s = \frac{230}{5} = 46$ V. …