# Resistors in Series

R1, R2 and R3 are three resistance-connected end to end across voltage source, **V**. VI. V2 and V3 are voltage drops in RI, R2 and R3 respectively **I** is the total current. From the fig we see that

*V _{T}= V_{I}+V_{2}+V_{3} ---> (1)*

We know that

*Vs=IR—> (2)*

Put eq (2) in eq (1) we get

*IR _{T}= IR_{1}+IR_{2}+IR_{3}--------> (3)*

*IR _{T} = I(R_{1}+R_{2}+R_{3}) —>(4)*

Divide both sides by I we get

*R _{T} = R_{1}+R_{2}+R_{3}*

In general

*R _{T} = R_{1}+R_{2}+R_{3}........................... R_{n}*

Where n=1,2,3,4,........

CONCLUSION

In series combination of resistance the total resistance is equal to the sum of all individual resistance.

## Resistance in series Characteristics

- In series circuit the current flows in each resistor is same.
*I*_{T}=I_{1}-I_{2}-I_{3} - In series circuit the total resistance is equal to the sum of all circuit resistance.
*R*_{T}= R_{1}+ R_{2}+ R_{3}................... R_{N} - In series circuit when the value of one resistor is increased as a result the total circuit resistance is increases.
- In series circuit there is the different voltage drop across each resister, which depends on the value of resister.
- In series circuit the total voltage is equal to the sum of voltage drop across each resister.
*V*_{T}= V_{1}+V_{2}+V_{3}*IR*_{T}= IR_{1}+ IR_{2}+ 1R_{3} - In series if there is fault in the one resister as a result the complete circuit will not work.
- In series circuit the total power is equal to the sum of all power, which are across the each resister.
*P*_{T}=P_{1}+P_{2}+P_{3}

As there are single path in this circuit so they are not used commonly.

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