Combination of Resistors
Combination of Resistors
- 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
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