Two identical resistors, each of resistance 20? are connected (i) in
parallel (ii) in series, in turn, to a battery of 10 V. Calculate the ratio of
power consumed in the combination of resistors in the two cases.

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Solution

Dear Student,
$E a c h r e s i s \tan c e i s 20 o h m a n d t h e r e a r e 2 r e s i s t o r s . S o i n p a r a l l e l c o n n e c t i o n w e g e t, R_{p} = \frac{20 \times 20}{20 + 20} = 10 o h m A g a i n i n c a s e o f s e r i e s c o n n e c t i o n w e g e t, R_{s} = 20 + 20 = 40 o h m S o t h e p o w e r c o n s u m e d i n s e r i e s c o m b i n a t i o n = \frac{V^{2}}{R_{s}} = \frac{100}{40} = 2.5 W a g a i n t h e p o w e r c o n s u m e d b y t h e c e l l i n p a r a l l e l c o m b i n a t i o n i s = \frac{V^{2}}{R_{p}} = \frac{100}{10} = 10 W$
So the ratio is =2.5:10 = 1:4 .
Regards

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Two identical resistors, each of resistance 20? are connected (i) in parallel (ii) in series, in turn, to a battery of 10 V. Calculate the ratio of power consumed in the combination of resistors in the two cases.

Two identical resistors, each of resistance 20? are connected (i) in
parallel (ii) in series, in turn, to a battery of 10 V. Calculate the ratio of
power consumed in the combination of resistors in the two cases.