Series Combination of Resistances

When two or more resistances are connected in series, they are arranged in a consecutive manner, with the current flowing through one resistance before passing through the next. In such a configuration, the total resistance is the sum of all the individual resistances.

Current through Each Resistance
In a series combination of resistances, the current passing through each resistance is the same. This is because the current has only one path to flow through, and it cannot split or divert to different paths. The same current flows through all the resistances.

To understand this concept, consider a simple series circuit with two resistances, R1 and R2, connected to a voltage source. Let's assume that the total current flowing through the circuit is I. According to Ohm's Law, the current flowing through each resistance can be calculated using the formula I = V/R, where V is the voltage across the resistance and R is the resistance value.

Since the resistances are connected in series, the voltage across each resistance is different. Let's say the voltage across R1 is V1 and the voltage across R2 is V2. However, the sum of these voltages will be equal to the total voltage of the circuit, which is V.

V = V1 + V2

Using Ohm's Law, we can rewrite this equation as:

IR1 + IR2 = V

Since the current passing through both resistances is the same, we can substitute I for both IR1 and IR2:

I(R1 + R2) = V

Simplifying the equation, we get:

I = V/(R1 + R2)

As the equation suggests, the current passing through each resistance is the same, regardless of their individual resistance values.

Voltage through Each Resistance
In contrast to the current, the voltage across each resistance in a series combination is different. This is because the total voltage of the circuit is divided among the individual resistances based on their resistance values.

Using the same example as before, the voltage across R1 can be calculated using Ohm's Law:

V1 = IR1

Similarly, the voltage across R2 can be calculated as:

V2 = IR2

Since the current passing through both resistances is the same, we can substitute I for both equations:

V1 = I * R1

V2 = I * R2

The voltage across each resistance depends on its resistance value. Hence, the voltage through each resistance is not the same in a series combination.

Conclusion
In summary, when resistances are connected in series:
- The current passing through each resistance is the same.
- The voltage across each resistance is different, based on their resistance values.