Internal Resistance Calculator

Online calculator for determining the internal resistance of a voltage source

Calculation

Result
Internal resistance:
Current through RL:


Good to know

What is internal resistance?

The internal resistance of a voltage source can be calculated by comparing two different load conditions. The open-circuit voltage and the loaded voltage are measured.

Circuit diagram
Voltage source with internal resistance

Voltage source with internal resistance and load resistance

Basic formulas
\[I = \frac{U_2}{R_L}\]
\[R_i = \frac{U_q - U_2}{I}\]
Variables
\(U_q\) = Source voltage (open-circuit)
\(U_2\) = Terminal voltage (loaded)
\(R_i\) = Internal resistance
\(R_L\) = Load resistance
\(I\) = Current through load resistance

Formulas for internal resistance

When a consumer is connected to an electrical source (e.g. a battery), a current flows, the strength of which essentially depends 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. However, there is an upper limit to the current. This limit is determined by the internal resistance of the battery.

The internal resistance can be calculated using two load conditions. First, the unloaded battery voltage (open-circuit voltage or source voltage) is measured. 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.

Current calculation

The current for a loaded power source can be calculated using the following formula:

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

Internal resistance

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

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

Practical example

Example: Battery internal resistance

Suppose we have a battery with an open-circuit voltage of 12 V. When the battery supplies a current of 2 A to a consumer, the voltage drops to 10 V.

Given:

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

Calculation:

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

The internal resistance of the battery is therefore 1 Ω.

Other important formulas

Terminal voltage
\[\displaystyle U_2 = U_q - (R_i \times I)\]

The terminal voltage is the measured voltage under load.

Short-circuit current
\[\displaystyle I_k = \frac{U_q}{R_i}\]

Theoretical maximum current in the event of a short circuit.

Variable 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

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