We have earlier studied that several capacitors can be connected in series or parallel combination to form a network. In same way several 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
Resistors are said to be connected in series combination. 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 in series combination.
If battery is connected across the series combination so as to maintain 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 divided 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 resistance of the series combination is always greater then the value of largest individual resistance.
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
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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 equivalent resistance would be reciprocal of