Parallel Connection of Resistors
Parallel Connection of Resistors
When two or more resistors are connected simultaneously between two points that is first ends of all the resistors are connected to one point and the all the second ends are connected to the other point, then they form a parallel combination. In this combination, the potential difference between the ends of all the resistances is same but the current is different in different resistance.
In this combination more than one resistance is connected as shown. In this type of circuit:
1. Equal potential difference across each resistance.
2. Total current flowing through the combination is equal to the sum of current flowing through each resistance.
3. Current through each resistance can be calculated using Ohm’s Law and is proportional to the value of resistance.
4. Equivalent resistance is less than resistance of any resistor in the circuit.. This is also known as minimum effective resistance
In the circuit given we have three resistance R1, R2 and R3 are connected in parallel and I1, I2 and I3 are the current flowing through each resistance respectively. If V is the potential difference across the combination the equivalent resistance can be calculated as
Total current is the sum of current flowing through each resistance,then
.....(i)
By Ohm s law,
.....(ii)
If R is the equivalent resistance, then
.....(iii)
Thus the values from equation (2) and (3) in (1) we get
Some important points regarding parallel combination of resistors are as follows :
Parallel combination of resistances is highly useful in circuits used in daily life as the circuits can have components of different resistances and different amounts of current can flow through them. The total resistance in a parallel circuit decreases which helps in the condition that each gadget has different resistances in a circuit and requires different amounts of current to operate. Parallel circuit divides the current among the components (electrical gadgets), so that they can have necessary amount of current to operate properly.
This is the reason of connecting electrical appliances in parallel combination in household circuit.
Illustration: In the circuit given below calculate the current flowing through each resistor.and verify the relationship of current in parallel connections.
Solution: In the circuit we have two resistance R1, R2 and R3 which are connected in parallel to battery of 9 V. The equivalent resistance can be calculated as
Substituting the value of resistance we get
Now as the battery is of 9 V, Then according to Ohm's Law
V= IR
Current through effective resistance (Rp ) is
For parallel combination of resistance, let us verify the relationship
L.H.S. = R.H.S
Hence the relation is verified.
In a circuit if three resistance of 3ohms each are connected in parallel then what is the net resistance | |||
| Right Option : C | |||
| View Explanation | |||
In a circuit if three resistance of 2 ohms each are connected in parallel then what is the net resistance | |||
| Right Option : C | |||
| View Explanation | |||
In a circuit if four resistance of 1 ohms, 2 ohms and 3 ohms and 4 ohms are connected in parallel then what is the net resistance | |||
| Right Option : B | |||
| View Explanation | |||
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