1.8 Internal Resistance of a Battery

Figure 1.8-1 shows a simple circuit containing a battery.

Figure 1.8-1 Internal Resistance of a Battery

When switch S is open—that is, when the circuit is in an open-circuit or no-load condition—the terminal voltage V [V] indicated by the voltmeter is equal to the electromotive force E [V] of the battery.
However, when switch S is closed and current begins to flow through the circuit, the terminal voltage V [V] becomes lower than E [V].

The voltage drop represented by E − V is caused by resistance within the battery, such as the resistance of its electrolyte. This resistance is called the internal resistance of the battery.

If the internal resistance is represented by r [Ω], the terminal voltage when the switch is closed is calculated using the following equation.

Therefore, the internal resistance r [Ω] can be calculated using the following equation.

According to Ohm’s law, the current I [A] is calculated as follows.

Substituting this expression into Equation (1.8-1) gives:

From Equation (1.8-4), when $R \gg r$,

and therefore $V \approx E$.
When the circuit is open, R can be regarded as approaching infinity. No current flows, and therefore V = E.

【Note】
As a battery ages, its internal resistance r generally increases. This produces a larger internal voltage drop when current flows and reduces the terminal voltage under load.
This is one of the principal reasons an aged or depleted battery can no longer supply the required voltage and current to a load.

About This Article

Reference
・Fundamentals of Electricity, Volume I, Corona Publishing Co., Ltd., by Toshio Utsunomiya, Hiroshi Takahashi, and Isao Izumi

※This article was prepared with reference to the source listed above and organized based on the author’s understanding.