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Series circuits
In the following circuit, three resistors of resistances R1, R2, and R3 are connected in series.
It has the following characteristics:
1- There exists a single path for the passage of electric current.
2- The same quantity of current exists at any point in the series circuit.
3- Equivalent resistance R is equal to the sum of all the resistance connected in series i.e.
R = R1 + R2 + R3
If the combination is replaced by its equivalent resistance in the circuit, then the amount of current flowing in the circuit remains the same.
Parallel circuits
In the circuit below, three resistors of resistance R1, R2, and R3 are connected in parallel.
It has the following characteristics.
1- All the resistors connected in parallel have the same potential difference across them.
2- As there are different paths for the current therefore there will be different values of current for each resistor, given by I1, I2 & I3 respectively such that the total current I is given by
I1 = I1+ I2 + I3
The equivalent resistance R of the combination of a parallel circuit is always than the least resistance of the parallel combination and is given by
1/R = 1/R1 + 1/R2 + 1/R3
Advantages of connecting lamps in parallel in lighting circuits
Lighting circuits in the home or other lighting circuits, such as the lighting circuit in a motor vehicle, are always connected in parallel.
There are two reasons for this.
Lamps are designed to operate at a fixed potential difference – no matter how many lamps are in parallel circuit, the potential difference accross them is always the supply potential diference. In a series circuit, the potential differenec is shared out between the lamps, so the more lamps there are, the smaller the potential difference accross each one and the dimmer each will be.
If the lamps are connected in series then they must be switched on or they must all be switched off, with a single switch. In the parallel circuit, the lamps can be switched separately as each lamp is in its own separate arm.