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# Equations of Transformers

### Equations of Transformers

The voltage across a coil in a transformer is proportional to the number of turns in the coil. We can find the efficiency of a transformer by comparing the input voltage with the output voltage.

A transformer has two coils. What is it that allows the transformer to increase or decrease the amount of voltage?

Recap from previous lessons

A transformer works by increasing or decreasing the **voltage** of an **alternating** current. It does this by using a **primary** **coil** of wire wrapped around a magnetic **iron** **core** to induce a current in a **secondary** **coil** of wire. The number of loops on the secondary coil determines if the voltage increases or decreases.

Which of these might be the correct symbols for **voltage** and **current** in the primary coil?

So current is represented by $I$ and voltage is represented by $V$. What do you think $N$ could represent?

So $V$ is voltage, $I$ is current and $N$ is number of loops or turns in the coil.

For the primary coil...

we use a little $_p$ to show when we are referring to the **primary coil**: $V_p$, $I_p$ and $N_p$

For the secondary coil...

we use a little $_s$ to show when we are referring to the **secondary coil**: $V_s$, $I_s$ and $N_s$

If a transformer is 100% efficient, what must be true about $V_{p}I_{p}$ and $V_{s}I_{s}$?

The primary coil in a transformer has **2 turns** and produces **3 Volts**. The secondary coil in the same transformer has **12 turns** and produces **18 Volts**.

How many times more turns are there in the secondary coil compared to the primary coil?

How many times more voltage is in the secondary coil compared to the primary coil?

If the secondary coils has **5 turns** and produces **8 volts**, then how many volts does the secondary coil produce if it has **25 turns**?

Which formula correctly describes the relationship between number of **turns** and amount of **voltage** produced in the primary and secondary coils?

The **ratio** of $V_p \space : \space V_s$ has to equal the **ratio** $N_p \space : \space N_s$. For example, if there are 2 turns in the first coil and 4 turns in the secondary coil, there are twice as many turns in the secondary coil as in the primary coil, so the secondary coil will also produce twice as much voltage as the primary coil.

We can express that like this: $\frac{V_{p}}{V_{s}}=\frac{N_{p}}{N_{s}}$

Now, if the primary coil has **3 turns** and produces **5 volts**, and the secondary coil has **9 turns**, then how many Volts does the secondary coil produce?