Physics, asked by govindp05, 4 months ago

Two resistors of resistances 6 Ω and 12 Ω, are connected first in series, and then in parallel in a circuit across a battery of 6 V. Calculate the ratio of the heat produced in the series combination to that of the parallel combination of resistors.

Answers

Answered by vanshikavikal448
65

 \huge  \red{ \fcolorbox{green}{grey}{required \: answer}}

resistors :- 6 ohm and 12 ohm

voltage :- 6 V

 \bold { \underline{ \underline \orange{answer}}} \orange→

2:9

 \bold { \underline{ \underline \orange{solution}}} \orange→

case (i)

when resistors are connected in series ;

Rs = R1 + R2

→ Rs = 6 + 12

→ Rs = 18 ohm

so, effective resistance in series combination is 18 ohm

we know that..

 \bold{ \color{blue} \: h =  \frac{ {v}^{2} t}{r}} \\

 \bold{ \implies \: h1 =  \frac{ {6}^{2}t }{18} } \\  \\ \bold{  \implies h1 =  \frac{36t}{18} }  \\  \\   \bold{\implies \: h1 = 2t} \:  \:  \:

so heat produced in series combination is 2t joule

case (ii)

when resistors are connected in parallel

we know that;

 \bold{ \frac{1}{Rp}  =   \frac{1}{r1}  +  \frac{1}{r2} } \\

 \bold { \tt{→ \:  \frac{1}{rp} =  \frac{1}{6}  +  \frac{1}{12} }} \:  \:   \:  \:  \:  \:  \\  \\  \bold{ \tt \implies \:  \frac{1}{Rp}  =  \frac{3}{12} }  \:  \:  \:  \:  \:  \:  \:  \:  \:  \\  \\  \bold{ \implies \: Rp =  \frac{12}{3} } \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \\  \\   \bold{\implies \: Rp = 4 \:  ohm } \:  \:  \:  \:

so, effective resistance in parallel combination is 4 ohm

and

 \bold{ \color{blue} \: h =  \frac{ {v}^{2} t}{r}} \\

 \bold{ \implies \: h2 =  \frac{ {6}^{2}t }{4} } \\   \\ \bold{  \implies \: h2 = \frac{36t}{4}  } \\  \\  \bold{ \implies \: h2 = 9t} \:  \:  \:

so heat produced in parallel combination is 9t joule.

  \bold{ \color{pink}ratio  \: of \: h1 \: and \: h2 \: } \\  \\ \bold \blue{  \frac{h1}{h2} =  \frac{2t}{9t}   } \\  \\  \bold{so \:  \:  \: h1 : h2 =2 : 9 }

hence, ratio of heat produced in the series combination to that of the parallel combination of resistors is 2:9

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