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Question

In the circuit shown in the figure, the heat produced in the $$5\Omega$$ resistor due to a current flowing in it, is $$10$$ calories per second. The heat produced in the $$4\Omega$$ resistor is?
1100126_bb5a638bc33340c4bf98033f5d378cd9.png


A
1 cal s1
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B
2 cal s1
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C
3 cal s1
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D
4 cal s1
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Solution

The correct option is B $$2$$ cal $$s^{-1}$$
$$\dfrac { { i }_{ 1 } }{ { i }_{ 2 } } =\dfrac { { R }_{ 2 } }{ { R }_{ 1 } } =\dfrac { 10 }{ 5 } =\dfrac { 2 }{ 1 } $$

Heat produced: $$\dfrac { H }{ t } ={ P }={ i }^{ 2 }R$$

$$\dfrac { { P }_{ 5 } }{ { P }_{ 4 } } =\left( \dfrac { { i }_{ 1 } }{ { i }_{ 2 } }  \right) ^{ 2 }\times \dfrac { 5 }{ 4 } =\left( \dfrac { 2 }{ 1 }  \right) ^{ 2 }\times \dfrac { 5 }{ 4 } =\dfrac { 5 }{ 1 } ={ P }_{ 4 }=\dfrac { 10 }{ 5 } =2cal/s$$

Physics
NCERT
Standard XII

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