Two heaters $A$ and $B$ have power rating of 1 kW and 2 kW, respectively. Those two are first connected in series and then in parallel to a fixed power source. The ratio of power outputs for these two cases is:

Option 1 - <math> <mrow> <mn>1</mn> <mo>:</mo> <mn>1</mn> </mrow> </math>

Option 2 - <math> <mrow> <mn>2</mn> <mo>:</mo> <mn>9</mn> </mrow> </math>

Option 3 - <math> <mrow> <mn>1</mn> <mo>:</mo> <mn>2</mn> </mrow> </math>

Option 4 - <math> <mrow> <mn>2</mn> <mo>:</mo> <mn>3</mn> </mrow> </math>

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Answered by

Alok Kumar Singh | Contributor-Level 10

6 months ago

Correct Option - 2

Detailed Solution:

Power Consumed $= P = \frac{V^{2}}{R}$

$\frac{P_{A}}{P_{B}} = \frac{R_{B}}{R_{A}}$

$R_{A} = 2 R_{B}$

For Series Combination

$P_{S} = \frac{V^{2}}{3 R_{B}}$

For Parallel Combination

$P_{P} = \frac{3 V^{2}}{2 R_{B}}$

$\frac{P_{S}}{P_{P}} = \frac{2}{9}$

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Two heaters A and B have power rating of 1 kW and 2 kW, respectively. Those two are first connected in series and then in parallel to a fixed power source. The ratio of power outputs for these two cases is:

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