Voltage Source Vs Current Source

Overview

Engineering reference data for Voltage Source Vs Current Source in electrical engineering.

Key Formulas

Ohm's Law

$V = IR$

Voltage = Current × Resistance.

Power

$P = VI = I^2R = V^2/R$

Electrical power.

Energy

$E = Pt$

Energy = Power × Time.

Variables

Symbol	Description	Unit
$V$	Voltage	V
$I$	Current	A
$R$	Resistance	Ω
$P$	Power	W

Behavior Characteristics

Voltage and current sources exhibit distinct behaviors under different load conditions:

• Voltage Source: Maintains a constant voltage ($V = V_s$) across its terminals regardless of load. Current is determined by the load resistance ($I = V_s / R_L$). It performs best into an open circuit (infinite $R_L$).

• Current Source: Maintains a constant current ($I = I_s$) through the load regardless of terminal voltage. Voltage is determined by the load resistance ($V = I_s \cdot R_L$). It performs best into a short circuit ($R_L = 0$).

Power Delivery

The power supplied by each source to a load resistance $R_L$ is:

For an ideal voltage source: $P = \frac{V_s^2}{R_L}$

For an ideal current source: $P = I_s^2 \cdot R_L$

Practical Considerations

Real sources have internal limitations:

• Real Voltage Source: Modeled as an ideal voltage source $V_s$ in series with an internal resistance $R_s$. Terminal voltage drops under load: $V_{terminal} = V_s - I \cdot R_s$.

• Real Current Source: Modeled as an ideal current source $I_s$ in parallel with an internal resistance $R_p$. Output current diverts through $R_p$ as terminal voltage increases: $I_{load} = I_s \cdot \frac{R_p}{R_p + R_L}$.

Equivalent Circuits

Every real voltage source (Thévenin equivalent) can be converted to a real current source (Norton equivalent) and vice versa:

$V_{\mathrm{Th}} = I_{\mathrm{N}} \cdot R_{\mathrm{Th}}$ $I_{\mathrm{N}} = \frac{V_{\mathrm{Th}}}{R_{\mathrm{Th}}}$

Where $R_{\mathrm{Th}} = R_{\mathrm{N}}$ represents the internal resistance of the source.

References

• Original Source