The basic difference between series and parallel connections of resistors lies in how the resistors are connected to each other and the resulting overall resistance.
1. Series Connection:
In a series connection, the resistors are connected end-to-end, forming a single path for the current to flow. The positive terminal of one resistor is connected to the negative terminal of the next resistor, and so on. The current through each resistor is the same.
- Resistance: The total resistance (R_total) in a series connection is the sum of the individual resistances (R1, R2, R3, ..., Rn). R_total = R1 + R2 + R3 + ... + Rn.
- Current: The current flowing through each resistor in a series connection is the same.
- Voltage: The voltage across the series connection is divided among the resistors. The voltage across each resistor depends on its resistance value.
2. Parallel Connection:
In a parallel connection, the resistors are connected such that both ends of each resistor are directly connected to the corresponding ends of other resistors, forming multiple parallel paths for the current to flow. The voltage across each resistor is the same.
- Resistance: The reciprocal of the total resistance (1/R_total) in a parallel connection is equal to the sum of the reciprocals of the individual resistances. 1/R_total = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn. The total resistance is always smaller than the smallest individual resistance.
- Current: The total current flowing into the parallel connection is divided among the resistors based on their resistance values. Each resistor carries a different amount of current.
- Voltage: The voltage across each resistor in a parallel connection is the same. The voltage across the parallel connection is equal to the applied voltage or the voltage source connected to the resistors.
In summary, series connection results in an additive increase in resistance and the same current flowing through each resistor. Parallel connection results in a reciprocal decrease in resistance, and the voltage across each resistor is the same while the total current is divided among the resistors.