voltage sources

voltage sources

1. What a Voltage Source Is

Voltage source maintains a specified voltage $V_s$ across its terminals independent of current drawn (ideal). Power $P = V_s·I$ can be positive (delivering) or negative (absorbing/charging).

• Ideal voltage source: $V = V_s$ constant for any $I$ (internal resistance $R_s=0$). $V$–$I$ is horizontal line.
• Practical voltage source: $V = V_s - I·R_s$ with series internal resistance $R_s$ (small, e.g., battery $R_s∼0.1$ Ω). Voltage drops slightly with load current.

2. Independent vs Dependent

• Independent: $V_s$ fixed (battery, lab supply, mains via transformer).
• Dependent (controlled): $V_s = k·V_x$ or $k·I_x$ where $k$ is gain, controlled by another voltage/current in circuit (used in amplifier models).

3. Characteristics and Symbols

Ideal voltage source: circle with + - , or battery symbol (long + , short -)
V = Vs (horizontal); I determined by external circuit: I= (Vs - V_load)/Rs

• Series: voltage sources in series add algebraically (consider polarity): $V_{eq}= Σ ±V_{si}$.
• Parallel: ideal voltage sources of different values cannot be paralleled (conflict → infinite current); practical with $R_s$ can, but shares current unequally.

4. Worked Examples

(a) Ideal 10V source across 5Ω load: I=2A, P=20W delivered ✓

(b) Practical 10V source with Rs=1Ω, load 5Ω: I=10/(1+5)=1.667A, terminal V=10 -1.667·1=8.33V (<10) ✓

(c) Two 10V sources series aiding: 20V; opposing: 0V ✓

(d) Need 12V from two 6V batteries series: Vs=12V, Rs sum.

5. Exam Points

• Define ideal vs practical ($V=V_s - I R_s$) — 5 marks, very frequent.
• Distinguish independent vs dependent — 3-5 marks, frequent.
• Show $V$ constant independent of $I$ — 3 marks.
• Series combination — 3 marks, frequent.