A battery of end E and internal resistance r is used in a circuit with a variable external resistance R. Find the value of R for which the power consumed in R is maximum.

Asked by prakriti12oct | 28th Jul, 2019, 11:07: PM

Expert Answer:

I equals fraction numerator E over denominator R plus r end fraction
S i n c e
P equals I squared R
T h e r e f o r e
P equals fraction numerator E squared R over denominator open parentheses R plus r close parentheses squared end fraction minus negative negative negative negative negative left parenthesis 1 right parenthesis
F o r space f i n d i n g space m a x i m u m space p o w e r space w e space h a v e space t o space a p p l y space t h e space c o n c e p t space o f space m a x i m a space a n d space m i n i m a
fraction numerator d P over denominator d R end fraction equals 0
w e space g e t
R equals r
O n space p u t t i n g space R equals r space i n space e q u a t i o n space left parenthesis 1 right parenthesis space w e space g e t
P subscript m a x end subscript equals fraction numerator E squared over denominator 4 r end fraction

Answered by Utkarsh Lokhande | 29th Jul, 2019, 08:21: AM