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 6A, 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. …