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Electrical

Load current from a Thevenin source

Current drawn by a resistive load from any linear DC network, once the network has been replaced by its Thevenin equivalent: an ideal voltage source in series with a resistance.

Ref
ELE-30
Rev
v1
Field
Electrical
Result
IL [A]

Any linear network seen from two terminals behaves like a voltage source Vth in series with a resistance Rth. A load RL connected to these terminals draws the current IL = Vth/(Rth + RL). Vth is the open-circuit voltage and the short-circuit current is Vth/Rth.

Current drawn by a resistive load from any linear DC network, once the network has been replaced by its Thevenin equivalent: an ideal voltage source in series with a resistance.

Calculator

Solve for
A
V
1100
Ω
0.1100
Ω
0.11,000
  • Short-circuit current, Vth/Rth3 A
  • Load voltage, ILRL6 V
  • Voltage lost inside the source, ILRth6 V

What drives the result

Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.

Load current (A) current value 1.5 A
VthThevenin (open-circuit) voltageKey driver
0.12512.5
RLLoad resistance
0.0122.93
RthThevenin resistance
0.1152.93
  • A 12 V source with 4 Ω of internal resistance drives 1.5 A into a 4 Ω load: 50 % of the short-circuit current of 3 A (exactly half when the load equals the source resistance).
  • A load much larger than Rth draws almost no current (an open circuit); a load much smaller draws nearly the short-circuit current.
Chart data as tables

Ranked variables

VariableTypical rangeLowest resultHighest resultSwing (A)Local stepChange in result
Vth Thevenin (open-circuit) voltage1 to 100 V0.12512.512.38+10%+10 %
RL Load resistance0.1 to 1,000 Ω0.011952.9272.915+10%−4.76 %
Rth Thevenin resistance0.1 to 100 Ω0.11542.9272.811+10%−4.76 %

Sweep of Load resistance

Load resistance (Ω)Load current (A)
0.12.927
0.31622.78
12.4
3.1621.675
100.8571
31.620.3369
1000.1154
316.20.03747
1,0000.01195

Sweep one variable

Load current (A)Hover, touch, or use the arrow keys on the chart
00.511.522.53 0.11101001000 Load resistance (Ω), log scale now 1.5

Variables and how each one contributes

IL

Load current

Result · A

What the equation gives you. Everything else feeds it.

Vth

Thevenin (open-circuit) voltage

V · typical 1 to 100

The open-circuit (Thevenin) voltage of the source, in volts. Raises the load current in direct proportion. Raising it by 1 V (to 13 V) moves the result by +8.33 %, from 1.5 to 1.625 A.

Rth

Thevenin resistance

Ω · typical 0.1 to 100

The Thevenin resistance seen from the load terminals, in ohms: the source’s internal resistance. Lowers the load current: more resistance in the source limits the current. Raising it by 0.5 Ω (to 4.5 Ω) moves the result by −5.88 %, from 1.5 to 1.412 A.

RL

Load resistance

Ω · typical 0.1 to 1,000

The load resistance, in ohms. Lowers the load current: a larger load resistance draws less current. Raising it by 0.5 Ω (to 4.5 Ω) moves the result by −5.88 %, from 1.5 to 1.412 A.

Worked example with the values above

  1. Total series resistance: Rth + RL = 4 + 4 = 8 Ω.
  2. Apply Ohm’s law: 12 V over 8 Ω.
  3. IL = 1.5 A.

Assumptions and limits

  • A linear circuit that can be replaced by a Thevenin equivalent: a voltage source Vth in series with a resistance Rth.
  • Steady DC conditions, or AC with purely resistive impedances.

Common mistakes

  • Using the load’s resistance as Rth: Rth belongs to the source side.
  • Forgetting that the Thevenin voltage is the open-circuit voltage, measured with the load removed.

Statistics and uncertainty

The current depends on the sum Rth + RL: a 5 % tolerance on each resistor gives about a 3.5 % error in the sum when they are equal, and so in the current. Measuring Vth and Rth by an open-circuit and a loaded test carries the meter’s errors as well.

Where it is used

  • Finding the current drawn from a battery, supply or sensor with internal resistance.
  • Reducing a complicated network to one equivalent loop.

Maths you need

  • Thevenin equivalent: a source and one resistance that replace the rest of the circuit
  • Ohm’s law: V = IR

Related formulas

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