voltage divider rule

voltage divider rule

1. What Voltage Divider Is

Voltage divider = series circuit rule to find how voltage splits across series resistors from total voltage, without solving whole circuit.

For two resistors $R_1,R_2$ in series, total voltage $V_{total}$ across them splits as:

i.e., voltage across a resistor = total × its resistance / sum. Larger $R$ gets larger share (proportional to $R$).

Derivation: same current

, then

2. For More Than Two Resistors

For $n$ series $R_i$, voltage across $R_k$:

3. Generalization to AC Impedance

For series impedances $Z_i$,

(phase matters).

4. Worked Examples

(a) 10V across series 2Ω+3Ω: V2Ω=10·2/5=4V, V3Ω=6V ✓ Check: 4+6=10, current 2A.

(b) Need to create 6V from 12V source with equal resistors: R1=R2 ⇒ V=6V each ✓

(c) Series 2Ω,3Ω,6Ω total 11Ω at 22V: V2=4V, V3≈6V, V6=12V ✓

(d) Loaded divider: divider R1,R2 with load RL across R2: R_eq2 = R2||RL, then V2 = Vtotal·R_eq2/(R1+R_eq2) < unloaded.

(e) Potentiometer is variable voltage divider.

(f) Why not for parallel? Parallel uses current divider.

5. Exam Points

• State $V_1=V·R_1/(R_1+R_2)$ for two series — 5 marks, very frequent (almost certain).
• Derive via $I=V/(R_1+R_2)$ — 3-5 marks, frequent.
• Solve numerical with 2 or 3 series, and loaded divider — 5-7 marks, very frequent.
• Distinguish from current divider (parallel) — 3 marks.