For any number of parallel branches, IT is divided into currents that are proportional to the conductance of the branches.
For a branch having conductance G:
I = G/Gt*It
G1 = 1/R1 = 1/10 Ω = 0.1 S
G2 = 1/R2 = 1/2 Ω = 0.5 S
G3 = 1/R3 = 1/5 Ω = 0.2 S
Fig. 7-5: Current divider with branch conductances G1, G2, and G3, each equal to 1/R. Note that S is the siemens unit for conductance. With conductance values, each branch I is directly proportional to the branch G.
The Siemens (S) unit is the reciprocal of the ohm (Ω)
GT = G1 + G2 + G3
= 0.1 + 0.5 + 0.2
GT = 0.8 S
I1 = 0.1/0.8 x 40 mA = 5 mA
I2 = 0.5/0.8 x 40 mA = 25 mA
I3 = 0.2/0.8 x 40 mA = 10 mA
KCL check: 5 mA + 25 mA + 10 mA = 40 mA = IT
Series Voltage Divider with Parallel Load Current
Voltage dividers are often used to tap off part of the applied voltage for a load that needs less than the total voltage.
Fig. 7-6: Effect of a parallel load in part of a series voltage divider. (a) R1 and R2 in series without any branch current. (b) A reduced voltage across R2 and its parallel load RL. (c) An equivalent circuit of the loaded voltage divider.
V1 = 40/60 x 60 V = 40 V
V2 = 20/60 x 60 V = 20 V
V1 + V2 = VT = 60 V (Applied Voltage)
The current that passes through all the resistances in the voltage divider is called the bleeder current, IB.
Resistance RL has just its load current IL.
Resistance R2 has only the bleeder current IB.
Resistance R1 has
both IL and IB.
Design of a Loaded Voltage Divider
Fig. 7-7: the Voltage divider for different voltages and currents from the source VT.
I1 through R1 equals 30 mA
I2 through R2 is 36 + 30 = 66 mA
I3 through R3 is 54 + 36 + 30 = 120 mA
V1 is 18 V to ground
V2 is 40 − 18 = 22 V
V3 is 100 V (Point D) − 40 = 60 V
R1 = V1/I1 = 18 V/30 mA = 0.6 kΩ = 600 Ω
R2 = V2/I2 = 22 V/66 mA = 0.333 kΩ = 333 Ω
R3 = V3/I3 = 60 V/120 mA = 0.5 kΩ = 500 Ω
NOTE: When these values are used for R1, R2, and R3 and connected in a voltage divider across a source of 100 V, each load will have the specified voltage at its rated current.