# internal resistance of a battery

Discussion in 'General Electronics Chat' started by u-will-neva-no, May 5, 2011.

1. ### u-will-neva-no Thread Starter Member

Mar 22, 2011
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Hello, I am slightly confused as to how one can measure the internal resistance of a battery. I thought to just use a multimeter set to"resistance", however I am pretty sure from elementary school that this is not allowed. I would like to know why this is not allowed and also how I could measure the internal resistance (without any fancy gadget, i.e something that I could easily use from a laboratory) Thankyou!

Apr 5, 2008
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3. ### russ_hensel Well-Known Member

Jan 11, 2009
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= Source or Output Impedance =

Input and output impedance can be very important but somewhat obscure ideas. This is meant to be a brief introduction to the ideas. First note that impedance is a generalization of the idea of resistance, where the value becomes a complex number due to contributions from capacitors and inductors. We will generally ignore this generalization and treat impedance as just resistance.

Consider a simple battery, perhaps a car battery. We often consider it a source of voltage say 12 volts. When we connect it to something else ( a headlight for example ) we may assume that the voltage of the battery is still 12 volts. This is fine for a first level approximation and is often used, sometimes we call it an ideal battery. But as we may know from experience when a load ( something like a headlight that draws current ) is added to a battery the battery's voltage drops a bit. If you want to do a simple experiment: turn on the headlights, then push in the cigarette lighter, and watch the headlights get just a bit dimmer because the load of the lighter drops the battery voltage. This is somewhat like being in a shower when someone else flushes the toilet.

There is a simple modification to the model of the ideal battery that makes it more like a real battery. Add an ideal resistor in series with the ideal battery. If the resistor is 0 ohms we are back to the ideal battery. This resistance, to the extent it exists is hidden inside the battery, so how do we measure it? There is a simple thought experiment to help understand it and variations of this experiment give practical methods for measurement.

Here is the experiment. Assume you have a volt meter and measure the voltage of the battery. Say 12 volts. Now add a resistor between the terminals of the battery as a load. Measure the voltage again. It will be lower say 11 volts. Try a lower value resistor, and again measure the voltage. Keep adjusting the resistor ( down to lower the voltage, up to raise the voltage until you get just half of 12 volts or 6 volts. At this point half the voltage of the battery is dropped by the internal resistance, and half by the external resistor you added. Hopefully you can see ( without equations or perhaps with equations ) that the internal and external resistor must have the same value. The internal resistance is also called the source resistance ( or impedance ).

( A practical note, The internal resistance of a car battery is quite low. Putting on an external resistor of the same value as the internal resistance will draw a lot of current and power from the battery. Your resistor must be large in physical size or may become red hot, the battery may get hot and be damaged: do not do this experiment unless you know enough to do it safely, in which case you can probably figure out how to do the experiment with a larger value of resistance ).

What applies to the output of the car battery also applies to any voltage source whether high or low voltage, whether alternating current or direct. In all cases adding a resistor as a load which drops the voltage in half determines the value of the source's internal resistance. With a bit of math you can determine the voltage drop for other values of load resistances, or determine the internal resistance from the measured voltage drop with an arbitrary load resistor.

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