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Two resistors of 12 ohm and 4 ohm are connected in parallel. The equivalent resistance is:
16 ohm
8 ohm
3 ohm
48 ohm
3 ohm
When resistors are connected in parallel, the reciprocal of the equivalent resistance is equal to the sum of the reciprocals of the individual resistances. For two resistors R1тАЛ and R2тАЛ, the equivalent resistance ReqтАЛ is calculated as ReqтАЛ=R1тАЛ+R2тАЛR1тАЛR2тАЛтАЛ.
When resistors are connected in parallel, the reciprocal of the equivalent resistance is equal to the sum of the reciprocals of the individual resistances. For two resistors R1тАЛ and R2тАЛ, the equivalent resistance ReqтАЛ is calculated as ReqтАЛ=R1тАЛ+R2тАЛR1тАЛR2тАЛтАЛ.
Think of parallel resistors like multiple checkout counters at a grocery store; having more counters open provides more pathways for shoppers to exit, which reduces the overall 'congestion' or resistance to the flow of people.
ReqтАЛ1тАЛ=R1тАЛ1тАЛ+R2тАЛ1тАЛ тАФ Definition of parallel resistance
ReqтАЛ=R1тАЛ+R2тАЛR1тАЛR2тАЛтАЛ тАФ Simplified formula for two resistors in parallel
In a parallel circuit, the voltage across each resistor remains the same, but the total current is divided among the branches. This effectively provides more paths for the current to flow, thereby reducing the total opposition (resistance) compared to any single resistor in the circuit. The formula is derived from Kirchhoff's Current Law, where the total current I=I1тАЛ+I2тАЛ.
The equivalent resistance in a parallel combination is always less than the smallest individual resistance in the group.
In this specific case, ReqтАЛ=12+412├Ч4тАЛ=1648тАЛ=3╬й.
Parallel circuits are used in household wiring to ensure that each appliance operates at the same voltage.
If one branch fails, the others continue to operate.
Each component receives the full source voltage.
Requires more wiring compared to a series circuit.
Total resistance decreases as more branches are added.
Domestic electrical wiring for lights and appliances.
Distribution systems in automobiles.
The SI unit of resistance is Ohm (╬й).
Option A (16 ohm) represents the result of a series combination (R1тАЛ+R2тАЛ=12+4=16).
Option B (8 ohm) is incorrect and lacks physical significance in this context.
C is correct тАФ The equivalent resistance of 12 ╬й and 4 ╬й resistors in parallel is 3 ╬й.
Always remember the shortcut for two resistors: Product divided by Sum. This saves significant time in competitive exams compared to using the reciprocal method.