- Introduction
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- Electric current and Current density
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- Drift Velocity
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- Relation between drift velocity and electric current
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- Ohm's Law and Resistance
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- Resistivity and conductivity
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- variation of resistivity with temperature
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- Current Voltage relations
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- Colour code of carbon resistors
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- Combination of Resistors

- We have earlier studied that sevral capacitors can be connected in series or parallel combination to form a network. In same way sevral resistor may be combined to form a network.

- Just like capacitors resistors can be grouped in series and parallel.

- Equivalent resistance of the combination of any number of resistors is a single resistance which draw same current as the combination of different resistances draw when the same potential difference is applied across it.

**(A) Resistors in Series**

- Resisors are said to be connected in series combinaton. If same current flows through each resistor when same potential difference is applied across the combination.

- Consider the figure given below

- In figure given above three resistors if resistance R
_{1}, R_{2}and R_{3}are connected ibn series combination.

- If battery is connected across the series combination so as to mintain potential difference V between points A and B, the current I would pass through each resistor.

- If V
_{1}, V_{2}andV_{3}is the potential difference across each resistor R_{1}, R_{2}and R_{3}respectively, then according to Ohm's Law,

V_{1}=IR_{1}

V_{2}=IR_{2}

V_{3}=IR_{3}

Since in series combination current remains same but potential is divieded so,

V=V_{1}+V_{2}+V_{3}

or, V=I(R_{1}+R_{2}+R_{3})

If R_{eq}is the resistance equivalent to the series combination of R_{1}, R_{2}and R_{3}then ,

V=IR_{eq}

where, R_{eq}=R_{1}+R_{2}+R_{3}

- Thus when the resistors are connected in series, equivalent resistance of the series combination is equal to the sum of individual resistances.

- Value of esistance of the series combination is always greater then the value of largest individual resisnces.

- For n numbers of resistors connected in series equivalent resistance would be

R_{eq}=R_{1}+R_{2}+R_{3}+...........................+R_{n}

**(B) Resistors in parallel**

- Resistors are said to be connected in parallel combination if potential difference across each resistors is same.

- Thus , in parallel combination of resistors potential remains the same but current is divided.

- Consider the figure given below

- Battery B is connected across parallel combination of resistors so as to maintain potential difference V across each resistors.Then total current in the circuit would be

I=I_{1}+I_{2}+I_{3}(16)

- Since potential difference across each resistors is V. Therefore, on applying Ohm's Law

V=I_{1}R_{1}=I_{2}R_{2}=I_{3}R_{3}

or,

From equation (16)

- If R
is the equivalent resistance of parallel combination of three resistors heaving resistances R _{1}, R_{2}and R_{3}then from Ohm's Law

V=IR_{eq}

or,

Comparing equation (16) and (17) we get

- For resistors connected in parallel combination reciprocal of equivalent resistance is equal to the sum of reciprocal of individual resistances.

- Value of equivalent resistances for capacitors connected in parallel combination is always less then the value of the smallest resistance in circuit.

- If there are n number of resistances connected in parallel combination, then quivalent resistance would be reciprocal of

Class 12 Maths Class 12 Physics