OHMLENS // EDA

Lesson 1.3 · Module 1: DC Physics & Network Theorems

Thevenin Equivalent & Why Batteries Sag Under Load

A real battery has a small resistance inside it. This lesson shows why a battery’s voltage drops (sags) when you draw a lot of current, as when a phone dies in the cold.

Think of it like this: Like a garden hose with a kink near the tap: the harder you draw water, the more pressure you lose at the kink.

The live, interactive simulation for this lesson opens here when JavaScript is on.

Key ideas

  • Every real battery behaves like a perfect source plus a small internal resistor.
  • The more current the load draws, the more voltage is lost inside the battery, turning into heat.
  • You get the most power out when the load resistance equals the internal resistance — but half of it is wasted as heat inside the battery.

Try this in the simulation

  • Lower the load resistance and watch the terminal voltage U_term sag.
  • Switch to the pulsed load to see how a radio burst makes the voltage dip.
  • Hover any wire or part in the circuit to see its live voltage and current. Click to pin the readout.

What is the Thevenin equivalent, and why does a battery voltage sag under load?

Any battery or power source behaves like a perfect voltage source in series with a small internal resistance. That pair is its Thevenin equivalent. When the load draws current, some of the voltage is lost across the internal resistance, so the voltage at the terminals sags. The heavier the load, the bigger the sag, and the lost energy turns into heat inside the battery.

What you’ll learn

  • How a real battery is modelled as a perfect source plus an internal resistance.
  • How to predict the terminal voltage for a given load current.
  • Why a battery sags more with a heavy or pulsed load, especially when it is old or cold.
  • When a load receives the most power, and why half of it is then wasted inside the source.

The formula, letter by letter

Uterm=Uoc−I Rint=3.00 V−391 mVPL,max=Uoc24Rint=150 mW at RL=Rint\begin{aligned}\htmlClass{mv mv-v_term}{\htmlStyle{font-size:1.37em}{\htmlData{sym=U_term}{U_{\mathrm{term}}}}} &= \htmlClass{mv mv-v_oc}{\htmlStyle{font-size:1.00em}{\htmlData{sym=U_oc}{U_{\mathrm{oc}}}}} - \htmlClass{mv mv-i}{\htmlStyle{font-size:1.21em}{\htmlData{sym=I}{I}}}\,\htmlData{sym=R_int}{R_{\mathrm{int}}} = \htmlData{funit=V,v=3}{\text{3.00 V}} - \htmlData{funit=mV,v=0.3913043478260869}{\text{391 mV}}\\ \htmlData{sym=P_Lmax}{P_{\mathrm{L,max}}} &= \frac{\htmlData{sym=U_oc}{U_{\mathrm{oc}}}^2}{4\htmlData{sym=R_int}{R_{\mathrm{int}}}} = \htmlData{funit=mW,v=0.15}{\text{150 mW}}\ \text{at}\ \htmlData{sym=R_L}{R_{\mathrm{L}}} = \htmlData{sym=R_int}{R_{\mathrm{int}}}\end{aligned}

Shown with this lesson’s starting values. In the simulation the numbers change as you move the sliders.

UtermU_{\mathrm{term}}
Terminal voltage (V · volt) : The voltage you actually get at a source’s terminals when it is loaded.
UocU_{\mathrm{oc}}
Open-circuit voltage (V · volt) : The voltage of a source with nothing connected: its full, unloaded voltage.
II
Current (A · ampere) : How much charge flows each second.
RintR_{\mathrm{int}}
Internal resistance (Ω · ohm) : The resistance hidden inside a battery or source.
PL,maxP_{\mathrm{L,max}}
Most power the load can get (W · watt)
RLR_{\mathrm{L}}
Load resistance (Ω · ohm)

Common questions

What is a Thevenin equivalent circuit?

It is a simple stand-in for a complicated source: one ideal voltage source in series with one resistor. From the outside it behaves exactly the same, which makes calculations much easier.

Why does my battery voltage drop when I connect a load?

The battery has an internal resistance. Current flowing through it causes a voltage drop inside the battery, so less voltage reaches the terminals. Bigger current means a bigger drop.

Why do old or cold batteries struggle with heavy loads?

Their internal resistance goes up, so the same current causes a larger drop, and the device sees a much lower voltage than a fresh battery would give.

Keep going

Words used in this lesson

Parts in this lesson

All lessons · How components work · Glossary