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Can you explain the answer of this question below:
When a number of resistors are connected in parallel, then their resultant resistance is ______________ the smallest individual resistance.
- A:Less than
- B:Sometime less and sometimes greater than
- C:Same as
- D:greater than
The answer is b.
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Can you explain the answer of this question below:When a number of res...
Resultant Resistance in Parallel Connection
When two or more resistors are connected in parallel, their resultant resistance is less than the smallest individual resistance. This is because of the fact that when resistors are connected in parallel, their equivalent resistance decreases.
Explanation:
When resistors are connected in parallel, the voltage across each resistor is the same and the current is divided among them. The total current flowing through the parallel combination is equal to the sum of the currents flowing through each resistor.
Using Ohm's law, the current through each resistor is given by:
I1 = V/R1, I2 = V/R2, I3 = V/R3, .... In = V/Rn
Where I1, I2, I3, ........In are the currents flowing through each resistor, V is the voltage across the parallel combination, R1, R2, R3, .......Rn are the resistances of each resistor.
The total current flowing through the parallel combination is given by:
IT = I1 + I2 + I3 + ......In
IT = V/R1 + V/R2 + V/R3 + ......V/Rn
Simplifying, we get:
IT = V(1/R1 + 1/R2 + 1/R3 + ......1/Rn)
The equivalent resistance of the parallel combination is given by:
1/Req = 1/R1 + 1/R2 + 1/R3 + ......1/Rn
Simplifying, we get:
Req = (R1 x R2 x R3 x ......Rn) / (R1 + R2 + R3 + ......Rn)
The above equation shows that the equivalent resistance of the parallel combination is less than the smallest individual resistance. This is because the denominator of the equation is always greater than the numerator, hence the equivalent resistance is always less than the smallest individual resistance.
Conclusion:
When two or more resistors are connected in parallel, their equivalent resistance is less than the smallest individual resistance. This is because when resistors are connected in parallel, their total current increases, resulting in a decrease in their equivalent resistance.
When two or more resistors are connected in parallel, their resultant resistance is less than the smallest individual resistance. This is because of the fact that when resistors are connected in parallel, their equivalent resistance decreases.
Explanation:
When resistors are connected in parallel, the voltage across each resistor is the same and the current is divided among them. The total current flowing through the parallel combination is equal to the sum of the currents flowing through each resistor.
Using Ohm's law, the current through each resistor is given by:
I1 = V/R1, I2 = V/R2, I3 = V/R3, .... In = V/Rn
Where I1, I2, I3, ........In are the currents flowing through each resistor, V is the voltage across the parallel combination, R1, R2, R3, .......Rn are the resistances of each resistor.
The total current flowing through the parallel combination is given by:
IT = I1 + I2 + I3 + ......In
IT = V/R1 + V/R2 + V/R3 + ......V/Rn
Simplifying, we get:
IT = V(1/R1 + 1/R2 + 1/R3 + ......1/Rn)
The equivalent resistance of the parallel combination is given by:
1/Req = 1/R1 + 1/R2 + 1/R3 + ......1/Rn
Simplifying, we get:
Req = (R1 x R2 x R3 x ......Rn) / (R1 + R2 + R3 + ......Rn)
The above equation shows that the equivalent resistance of the parallel combination is less than the smallest individual resistance. This is because the denominator of the equation is always greater than the numerator, hence the equivalent resistance is always less than the smallest individual resistance.
Conclusion:
When two or more resistors are connected in parallel, their equivalent resistance is less than the smallest individual resistance. This is because when resistors are connected in parallel, their total current increases, resulting in a decrease in their equivalent resistance.
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Community Answer
Can you explain the answer of this question below:When a number of res...
Supposing we take the resistances to be 1ohm 2 ohm and 3 ohm ...So the resulting resistances in parallel turns to be around 0.54 ohms
Also if we take resistances to be 2 ohm 3 ohm and 5 ohm then the resulting resistances in parallel is around 0.9 ohms
And in both cases the Rp is less than the smallest individual resistance....
Therefore the correct answer is A
Also if we take resistances to be 2 ohm 3 ohm and 5 ohm then the resulting resistances in parallel is around 0.9 ohms
And in both cases the Rp is less than the smallest individual resistance....
Therefore the correct answer is A
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