Voltage divider rule and current divider rule

Voltage divider rule

Suppose there are a few resistors in series in a circuit with which an emf source (like a battery) is connected. Now how to find the voltage drops in each resistor? One way is to find the current first by using the formula I = E/(Req +r). Here Req stands for equivalent resistant of the external circuit and r is the internal resistance of the battery. After evaluating the current you can now use Ohm’s law (V = IR) to find the individual voltage drop across each resistor including the internal resistance.

Another way is using Voltage divider rule. Suppose there are two external resistors R1 and R2 and the internal resistance is r. So using the voltage divider rule the voltage drop across R1 is E*R1/(R1+R2+r). The same way voltage drops across R 2 and r can be found as well.

Current divider rule

Now about the current divider rule. In this case, the resistors have to be connected in parallel. Suppose two resistors (and probably this rule works only for two resistors only, not for three resistors) are connected in parallel. And the magnitude of the total current flowing through them is I. then by using current divider rule, the current through R1 is I1 = R2 * I /(R1 + R2) and that through R2 is I2 = R1 * I / (R1 + R2). This law/rule indicates that current in any parallelly connected resistor is inversely proportional to its resistance, which is evident from Ohm’s law. This is because, the voltage drop across the parallel combination is constant in this case.