Two heaters <math> <mrow> <mi>A</mi> </mrow> </math> and <math> <mrow> <mi>B</mi> </mrow> </math> 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:

Power Consumed = P = V 2 R  P A P B = R B R A  R A = 2 R B For Series Combination P S = V 2 3 R B For Parallel Combination P P = 3 V 2 2 R B  P S P P = 2 9

Two heaters <math> <mrow> <mi>A</mi> </mrow> </math> and <math> <mrow> <mi>B</mi> </mrow> </math> &nbsp;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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Overview Physics Current Electricity Physics Class 12th

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 -

$1 : 1$

Option 2 -

$2 : 9$

Option 3 -

$1 : 2$

Option 4 -

$2 : 3$

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1 Answer

Answered by

alok kumar singh | Contributor-Level 10

a month 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

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

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

Power Consumed <math> <mrow> <mo>=</mo> <mi>P</mi> <mo>=</mo> <mfrac> <mrow> <msup> <mrow> <mi>V</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mi>R</mi> </mrow> </mfrac> </mrow> </math>  <math> <mrow> <mfrac> <mrow> <msub> <mrow> <mi>P</mi> </mrow> <mrow> <mi>A</mi> </mrow> </msub> </mrow> <mrow> <msub> <mrow> <mi>P</mi> </mrow> <mrow> <mi>B</mi> </mrow> </msub> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <msub> <mrow> <mi>R</mi> </mrow> <mrow> <mi>B</mi> </mrow> </msub> </mrow> <mrow> <msub> <mrow> <mi>R</mi> </mrow> <mrow> <mi>A</mi> </mrow> </msub> </mrow> </mfrac> </mrow> </math>  <math> <mrow> <msub> <mrow> <mi>R</mi> </mrow> <mrow> <mi>A</mi> </mrow> </msub> <mo>=</mo> <mn>2</mn> <msub> <mrow> <mi>R</mi> </mrow> <mrow> <mi>B</mi> </mrow> </msub> </mrow> </math> For Series Combination <math> <mrow> <msub> <mrow> <mi>P</mi> </mrow> <mrow> <mi>S</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msup> <mrow> <mi>V</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>3</mn> <msub> <mrow> <mi>R</mi> </mrow> <mrow> <mi>B</mi> </mrow> </msub> </mrow> </mfrac> </mrow> </math> For Parallel Combination <math> <mrow> <msub> <mrow> <mi>P</mi> </mrow> <mrow> <mi>P</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mn>3</mn> <msup> <mrow> <mi>V</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>2</mn> <msub> <mrow> <mi>R</mi> </mrow> <mrow> <mi>B</mi> </mrow> </msub> </mrow> </mfrac> </mrow> </math>  <math> <mrow> <mfrac> <mrow> <msub> <mrow> <mi>P</mi> </mrow> <mrow> <mi>S</mi> </mrow> </msub> </mrow> <mrow> <msub> <mrow> <mi>P</mi> </mrow> <mrow> <mi>P</mi> </mrow> </msub> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> </mrow> <mrow> <mn>9</mn> </mrow> </mfrac> </mrow> </math>