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What is the equivalent resistance of three 10 ohm resistors connected in parallel?
3.33 ohms
10 ohms
30 ohms
0.33 ohms
33 ohms
When resistors are connected in parallel, the reciprocal of the equivalent resistance is equal to the sum of the reciprocals of individual resistances. For three identical resistors of 10╬й, the equivalent resistance is calculated as ReqтАЛ1тАЛ=101тАЛ+101тАЛ+101тАЛ=103тАЛ.
When resistors are connected in parallel, the reciprocal of the equivalent resistance is equal to the sum of the reciprocals of individual resistances. For three identical resistors of 10╬й, the equivalent resistance is calculated as ReqтАЛ1тАЛ=101тАЛ+101тАЛ+101тАЛ=103тАЛ.
Think of a highway toll plaza with multiple booths open; having more lanes (resistors) open allows traffic (current) to pass through more easily, reducing the overall 'bottleneck' (resistance).
For parallel circuits, remember that the 'total resistance drops' (it is always less than the smallest individual resistor).
ReqтАЛ1тАЛ=R1тАЛ1тАЛ+R2тАЛ1тАЛ+R3тАЛ1тАЛ тАФ Reciprocal formula for parallel resistance
ReqтАЛ=nRтАЛ тАФ Simplified formula for n equal resistors in parallel
In a parallel circuit, the voltage across each branch remains the same, but the total current is divided among the branches. This effectively creates multiple paths for the electrons to flow, which reduces the total opposition to the current, resulting in a lower equivalent resistance than any of the individual resistors. According to Ohm's Law and Kirchhoff's laws, for n equal resistors connected in parallel, the equivalent resistance is ReqтАЛ=nRтАЛ.
Equivalent resistance in parallel is always less than the smallest individual resistance.
Voltage across each parallel resistor is identical.
Total current is the sum of currents through individual branches.
If one component fails, the others continue to function.
Each device operates at the full source voltage.
Cannot provide different voltages to components without additional regulators.
Requires more wiring and space compared to a series connection.
Domestic electrical wiring for appliances
Car electrical systems
Calculation: ReqтАЛ=310тАЛтЙИ3.33╬й.
Option B (10 ohms) would be the answer if resistors were in series (10+10+10=30 is incorrect for series, which should be 30; 10 is the value of one resistor).
Option C (30 ohms) is the result of adding them in series (10+10+10=30╬й).
A is correct тАФ The equivalent resistance of three identical resistors in parallel is one-third of the value of a single resistor, resulting in 3.33╬й.
Always check if the combination is 'series' or 'parallel' before calculating; remember that parallel resistance always decreases total impedance while series resistance always increases it.