Current Dividers and Current Division Circuits
A current divider circuit divides the current into multiple parallel paths. In parallel paths, the voltage still remains the same irrespective of the distribution of current in them. Due to the constant voltage, there is no need to evaluate voltages at each node of the circuit. All the parallel branches connected with the same voltage supply will have the same voltage across their ends.
This concept is illustrated below:
In the above circuit:
But:
Where: 
Derivation of Current Divider Formula
Branch currents in parallel networks can be easily calculated through a standardized current division formula. The stepwise derivation for individual branch currents is provided below.
Total current through the above circuit is given by:
Substituting the expressions for IR1 and IR2:
Re-arranging for VS:
Substituting Vs again in the above expression of IR1:
Substituting VS again in the above expression of IR2:
Current Divider Formula Vs Voltage Divider Formula
A voltage divider circuit is simply a series combination of resistances connected with a voltage source. The voltage drops vary across each resistance in series while the same current flows throughout the circuit as there is only a path for current to flow from and back to the source. Differences between the current divider and voltage divider formula are tabulated below:
| Current Divider Formula | Voltage Divider Formula |
| Resistors are connected in parallel arrangement. | Resistors are connected in series arrangement. |
| Current divider demonstrates division of current into multiple parallel branches of circuit. | Voltage divider demonstrates division of voltage into multiple voltage drops across circuit elements in series. |
| Current divider formula applies when there are different currents flowing in the circuit. | Voltage divider formula applies when there are different voltage drops in the circuit. |
| Magnitude of current varies across every resistor. | Voltage drops vary across every resistor. |
| All current magnitudes when added, they shall equal source current. | All voltage drops when added, they shall equal source voltage. |
Conductance
Conductance is calculated by reciprocating the resistance. In other words, it is the inverse of resistance. The units of conductance are mho, which is the inversion of the units of resistance, ohm. The conductance units are also denoted by Siemens (S).
Based on the above definition, we can write:
Parallel Conductance
Parallel conductance also behaves opposite to parallel resistance in a parallel network. Individual conductance is simply added as resistors are added in a series combination. Therefore:
Whereas:
Current Divider Formula for Conductance
The current divider formula also applies if conductance is known:
As we know:
Ohm’s law can be expressed as:
Substituting VS:
Similarly, IR2:
Example
Consider three resistances with 2k, 6k, and 4k in the circuit below. Find branch current, total current, and equivalent resistance of the below network.
Branch current through R1:
Also, we know:
Where IT can be calculated by finding Req:
IT can also be calculated through the sum of all branch currents:
Using the second set of equations, calculations can be more simplified, as below:
Finding IR1:
For IR2:
For IR3:
Now, finding Req:
Conclusion
A current divider can be any circuit with two or more parallel branches in them. The current distributes as it passes through each branch. Therefore, current division formulas for calculating branch currents are applied to evaluate these circuits. Moreover, current dividers do not affect voltage, since the voltage across any branch will remain the same.
