Internal resistance of electrical power sources

The internal resistance of an electrical source can be calculated by comparing two different load conditions. To do this, measure the open circuit voltage without load. Then the voltage source is loaded with a resistor and the loaded voltage is measured. With the determined data you can calculate the internal resistance of the voltage source on this page.

internal resistance calculator  Input Delete Entries Open circuit voltage µV mV V kV Loaded voltage µV mV V kV Load Resistance mΩ Ω kΩ MΩ Decimal places 0 1 2 3 4 6 8 10  Result Internal resistance Current

Formulas for internal resistance

If a consumer is connected to an electrical source (e.g. a battery), a current flows, the strength of which depends essentially on the voltage of the battery and the value of the consumer's resistance. The smaller the resistance value, the greater the current flowing in the circuit. An upper limit is set for the current. This limit is determined by the internal resistance of the battery.

The internal resistance can be calculated using two load conditions. We first measure the unloaded battery voltage (open circuit voltage or source voltage). Then the battery is loaded with a resistor. The loaded voltage is then measured. The current can be measured or calculated using the formula below. The internal resistance of the battery can be calculated using the calculator above from the difference between the two voltages and the current.

The formulas below are used for the calculation.

The current when the power source is under load can be calculated using the following formula:

\[\displaystyle I=\frac{U_2}{R_L}\]

The internal resistance can then be calculated using the current and the voltage difference.

\[\displaystyle R_i=\frac{U_q-U_2}{I}\]

Legend

\(U_q \)	Source voltage
\(U_2\)	Terminal voltage
\(R_{i} \)	Internal resistance
\(R_{L} \)	Load resistance
\(I \)	Current with load resistance
\( I_k \)	Short circuit current

Example:

Suppose we have a battery with an open circuit voltage of 12 V. If the battery supplies a current of 2 A to a consumer, the voltage drops to 10 V. We can calculate the internal resistance of the battery as follows:

• \(U_q=12 V\)
• \(U_2=10V\)
• \(I=2A\)

Then the formula is:

\[R_i=\frac{12 V-10V}{2A}=\frac{2V}{2A}=1Ω\]

The internal resistance of the battery is therefore 1 Ω.

More formulas

Terminal voltage

\[\displaystyle U_2=U_q-(R_i·I) \]

Short circuit current

\[\displaystyle I_k=\frac{ U_q}{R_i} \]

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