Direct current circuit

Fig. 1 Simple direct current circuit with power source and load

We consider a very simple circuit where a direct current power source such as batteries is connected to a load like light bulbs.

Since power sources have internal impedance (footnote 1), we take the value as a pure resistance Rs, and take the load as a pure resistance Rl. There are no circuits without inductance or capacitance, however there are many situations where inductance and capacitance can be ignored, and most useful circuits fall into this category.

Furthermore, we also ignore attenuation from cables connecting the power source and load. This means loss from cables is much smaller than loss from the load or internal inpedance of the power source, but energy transmission is usually conducted under this condition.

The problem is whether the voltage on the load can be considered as

  V = E * Rl / (Rs + Rl)
  Here,
	V = voltage on load Rl (V)
	E = Power source voltage (V)
	Rl = load resistance (Ohm)
	Rs = internal resistance of power source (Ohm)

Footnote 1 - Necessity of internal resistance in power source

If a power source without internal resistance exists, by lowering the load resistance, an unlimited amount of energy can be extracted. The derivation is simple, and is worth a try.