A series circuit is one in which several resistances are connected one after the other. Such connection is also called end to end connection or cascade connection. There is only one path for the flow of current.

Consider resistor shown in the Fig. 1. The resistance R

Now let us study the voltage distribution

_{1}, R_{2}and R_{3}are said to be in series. The combination is connected across a source of a voltage V volts. Naturally the current flowing through all of them is same indicated as I amperes. e.g. the small chain of small lights, used for the decoration purposes is good example of series combination.Fig. 1 A series circuit |

Let V

_{1}, V_{2 }and V_{3}be the voltages across the terminals of resistances R_{1}, R_{2}and R_{3 }respectively,Then V = V

Now according to Ohm's law V

Current through of them is same i.e. I

V = I R

Applying Ohm's law to overall circuit

_{1 }+V_{2}+ V_{3}Now according to Ohm's law V

_{1}= I R_{1}, V_{2 }= I R_{2}, V_{3 }= I R_{3 }Current through of them is same i.e. I

V = I R

_{1 }+ I R_{2 }+ I R_{3 }= I (R_{1}+R_{2}+R_{3})Applying Ohm's law to overall circuit

V = I R

_{eq} Where R

_{eq }= Equivalent resistance of the circuit, by comparison of tow equations, R

_{eq }= R_{1 }+ R_{2 }+ R_{3 } i.e. total or equivalent resistance of the series circuit is arithmetic sum of the resistances connected in series

For n resistances in series, R = R

_{1 }+ R_{2 }+ R_{3 }+.......+ R_{n }**Characteristic of series circuits**

1) The same current flows through each resistance.

2) The supply voltage V is the sum of the individual voltage drops across the resistances.

V = V

_{1 }+V_{2}+_{ }..... + V_{n }3) The equivalent resistance is equal to the sum of the individual resistances

4) The equivalent resistance is the largest of all the individual resistances.

i.e R >R

_{1 }, R >R_{2 }, ..........R > Rn

**2. Inductors in series** Consider in the Fig. 2(a). Tow inductors L

_{1 }and L_{2 }are connected in series. The current flowing through L_{1 }and L_{2 }are i_{1 }_{ }and i_{2 }while voltages developed across L_{1 }and L_{2 }are V_{L1 }and V_{L2 }respectively. The equivalent circuit as shown in the Fig. 2(b).Fig. 2 |

For series combination,

i = i

_{1 }= i_{2 }and V

_{L }= V_{L1 }+ V_{L2 }**.**L

^{.}._{eq }di/dt = L

_{1 }di/dt + L

_{2 }di/dt

**.**L

^{.}._{eq }di/dt = (L

_{1 }+L

_{2 }) di/dt

**.**L

^{.}._{eq }= L

_{1 }+L

_{2 }

That means, equivalent inductances of the series combination of tow inductances is the sum of inductances connected in series

The total equivalent inductances of the series circuit is the sum of the inductances connected in series.

For n inducatances in series,

L

_{eq }= L_{1 }+ L_{2}+ L_{3}+ ............+ L_{n}

**3. Capacitors in series** Consider the Fig. 3(a). Tow capacitors C

_{1 }and C_{2 }are connected in series. The current flowing through and voltages developed across C_{1 }and C_{2 }are i_{1}, i_{2 }and V_{C1 }and V_{C2 }respectively. The equivalent circuit is shown in the Fig. 3(b).Fig. 3 |

For series combination,

i = i

_{1}= i_{2 }and V

_{C }= V_{C1 }+ V_{C2 } But i = i

_{1}= i_{2 } That means, reciprocal of equivalent capacitor of the series combination is the sum of the reciprocal of individual capacitances.

The reciprocal of the total equivalent capacitors of the series combination is the sum of the reciprocols of the individual capacitors, connected in series,

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