Voltage divider

Voltage divider rule finds the voltage over a load in electrical circuit, when the loads are connected in series.

Voltage divider rule for DC circuit

For a DC circuit with constant voltage source V_T and resistors in series, the voltage drop V_i in resistor R_i is given by the formula:

$V_i=V_T\: \frac{R_i}{R_1+R_2+R_3+...}$

V_i - voltage drop in resistor R_i in volts [V].

V_T - the equivalent voltage source or voltage drop in volts [V].

R_i - resistance of resistor R_i in ohms [Ω].

R₁ - resistance of resistor R₁ in ohms [Ω].

R₂ - resistance of resistor R₂ in ohms [Ω].

R₃ - resistance of resistor R₃ in ohms [Ω].

Voltage source of V_T=30V is connected to resistors in series, R₁=30Ω, R₂=40Ω.

Find the voltage drop on resistor R₂.

V₂ = V_T × R₂/ (R₁+R₂) = 30V × 40Ω / (30Ω+40Ω) = 17.14V

For an AC circuit with voltage source V_T and loads in series, the voltage drop V_i in load Z_i is given by the formula:

$V_i=V_T\: \frac{Z_i}{Z_1+Z_2+Z_3+...}$

V_i - voltage drop in load Z_i in volts [V].

V_T - the equivalent voltage source or voltage drop in volts [V].

Z_i - impedance of load Z_i in ohms [Ω].

Z₁ - impedance of load Z₁ in ohms [Ω].

Z₂ - impedance of load Z₂ in ohms [Ω].

Z₃ - impedance of load Z₃ in ohms [Ω].

Voltage source of V_T=30V∟60° is connected to loads in series, Z₁=30Ω∟20°, Z ₂=40Ω∟-50°.

Find the voltage drop in load Z₁.

V₂ = V_T × Z₁/ (Z₁+Z₂)

= 30V∟60° × 30Ω∟20° / (30Ω∟20°+40Ω∟-50°)

= 30V∟60° × 30Ω∟20° / (30cos(20)+j30sin(20)+40cos(-50)+j40sin(-50))

= 30V∟60° × 30Ω∟20° / (28.19+j10.26+25.71-j30.64)

= 30V∟60° × 30Ω∟20° / (53.9-j20.38)

= 30V∟60° × 30Ω∟20° / 57.62Ω∟-20.71°

= (30V×30Ω/57.62Ω) ∟ (60°+20°+20.71°)

= 15.62V∟100.71°