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Two equal resistors, each of resistance R, connected in series across a voltage source V dissipate power P. What would be the power dissipated in the same resistors when they are connected in parallel across the same voltage source?
- a)4P
- b)2P
- c)16P
- d)P
Correct answer is option 'A'. Can you explain this answer?
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Two equal resistors, each of resistance R, connected in series across ...
Explanation:
When resistors are connected in series:
- In series connection, the total resistance is equal to the sum of individual resistances: Rs = R + R = 2R.
- The current flowing through each resistor is the same, I = V / Rs.
- The power dissipated by each resistor is given by P = I^2 * R = (V / Rs)^2 * R = V^2 * R / (2R)^2 = V^2 * R / 4R^2 = V^2 / 4R.
When resistors are connected in parallel:
- In parallel connection, the total resistance is given by Rp = R / 2.
- The current flowing through each resistor is split between them, so the current through each resistor is I = V / R.
- The power dissipated by each resistor is given by P = I^2 * R = (V / R)^2 * R = V^2 / R.
Comparing the power dissipated:
- Power dissipated in series connection: V^2 / 4R.
- Power dissipated in parallel connection: V^2 / R.
Therefore, the power dissipated in parallel connection is 4 times greater than the power dissipated in series connection. Hence, the correct answer is option 'A'.
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Two equal resistors, each of resistance R, connected in series across ...
Let R be the resistance of the identical two resistors. When they are connected in series across a voltage source V, the equivalent resistance of the combination is 2R and then total power dissipated by the resistors will be P = V2/2R.
When they are connected in parallel across the same voltage source V, the equivalent resistance of the combination is R/2, and then total power dissipated by the resistors will be V2/(R/2) = 4V2/2R = 4P.
When they are connected in parallel across the same voltage source V, the equivalent resistance of the combination is R/2, and then total power dissipated by the resistors will be V2/(R/2) = 4V2/2R = 4P.
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Two equal resistors, each of resistance R, connected in series across a voltage source V dissipate power P. What would be the power dissipated in the same resistors when they are connected in parallel across the same voltage source?a)4Pb)2Pc)16Pd)PCorrect answer is option 'A'. Can you explain this answer?
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