A battery of e.m.f. 15 V and internal resistance 2 $Ω$ is connected to two resistors of resistances 4 ohm and 6 ohm joined in series. Find the electrical energy spent per minute in 6 ohm resistor.

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Solution

Given,
E.m.f of battery , V=15 V
$Internal space resistance space of space battery comma R subscript B equals 2 space o h m R e s i s a n c e space g i v e n space i n space c i r c u i t space comma R subscript 1 equals 4 space o h m space comma space R subscript 2 equals 6 space o h m W h e n space r e s i s t o r s space a r e space c o n n e c t e d space i n space s e r i e s space comma E q u i v a l e n t space r e s i s tan c e space space comma space R equals R subscript B plus R subscript 1 plus R subscript 2 equals 12 space o h m c u r r e n t space i n space t h e space c i r c u i t space comma I equals 15 over 12 equals 1.25 A N o w space v o l t a g e space a c r o s s space r e s i s t o r space R subscript 2 space comma space V subscript 2 equals I R equals 1.25 cross times 6 equals 7.50 space V T i m e comma t equals 1 space m i n space equals 60 space s e c E n e r g y space a c r o s s space R subscript 2 comma space E equals fraction numerator V squared t over denominator R end fraction equals fraction numerator 7.5 squared cross times 60 over denominator 6 end fraction equals 562.5 space J$

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