# Conservation of energy in transformers

How does energy remain conserved in a transformer if emf is increasing, or decreasing? Does the current decreases to accomodate? Does Ohm's law still hold here? Although we know, Ohm's law is not universal.

• energy is conserved in every energy consuming process in this world – agha rehan abbas Jun 28 '14 at 17:37
• I dont ask whether it remains conserved or not, I asked, how does it remain conserved – Rohit Jun 28 '14 at 17:51
• – Always Confused Jun 29 '16 at 19:20

If you're concerned about Ohm's law, you might be getting a little muddled in your thoughts (don't worry, I only know this because I've had my turn at being muddled before on this point!)

Ohm's law doesn't describe a transformer: Ohm's law may apply to whatever load you connect to the transformer; if so, then Ohm's law combines with the transformer law $V_P\, I_P = V_S\, I_S$ to yield the concept of reflected impedance (as I talk about in the linked answer): a load with impedance $\mathcal{Z}$ connected across the transformer's secondary appears as the load $\left(\frac{N_S}{N_P}\right)^2\,\mathcal{Z}$ at the primary. This generalises to:

$$Z_P \approx \left(Z_{T1}^{-1}+\left(Z_{T2}+\left(\frac{N_S}{N_P}\right)^2\,\mathcal{Z}\right)^{-1}\right)^{-1}$$

in a real transformer, where $Z_{T1}$ and $Z_{T2}$ model the transformer's own ohmic losses and energy storage capacity.

The transformer equation itself can be thought of as either:

1. A statement of conservation of energy; OR
2. A statement that the same flux links the primary and secondary and the consequences of applying (a) Ampère's law to a flux loop threading both primary and secondary to get the current ratio from and (b) Faraday's law to flux time variation, to get the voltage ratio.

Yes you're right. Wikipedia calls this the transformer equation: $$\frac{V_P}{V_S} = \frac{I_S}{I_P}=\frac{N_\text{P}}{N_\text{S}}=\sqrt{\frac{L_P}{L_S}}$$ $P$ and $S$ denote primary and secondary, respectively. $V,I,N$ and $L$ are emf, current, winding number and inductance. Keeping this ratio constant assures that the power $P=V_SI_S=V_PI_P$ is the same on either side.

• Yes, I figured that out long ago. But what I could figure out since long was that, wouldnt it violate our old pal Ohm's law? – Rohit Jul 4 '14 at 1:51
• @Rohit: No, this becomes a voltage to be considered. So if you plug a $10:1$ stepdown transformer into a $120VAC$ outlet, you have $12VAC$ at the output. If you connect that across a $2\Omega$ resistor, you will draw $6 AAC$. That will draw $0.6 AAC$ from the wall. The back emf is then $120VAC$ and all is well. – Ross Millikan Aug 2 '14 at 2:38
• @Rohit If you're concerned about how Ohm's law fits in to conservation of energy, please put that in your question. – BMS Sep 8 '14 at 6:00