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Home / Doubts and Solutions/JEE/Physics

the resistant R is given by relation R=V/I if potential difference V is 100+or_5V and current 1 is 10+or_0.2A calucate the percentage error is R

Asked by futureisbright051101 5th March 2018, 7:34 PM
Answered by Expert
Answer:
begin mathsize 12px style R space equals space V over I semicolon w i t h space e r r o r space i n space m e a s u r e m e n t space o f space V space a n d space I comma space R space w i t h space e r r o r space i s space g i v e n space b y R plus-or-minus capital delta R space equals space fraction numerator V plus-or-minus capital delta V over denominator I plus-or-minus capital delta I end fraction space equals space fraction numerator V open parentheses 1 plus-or-minus begin display style fraction numerator capital delta V over denominator V end fraction end style close parentheses over denominator I open parentheses 1 plus-or-minus begin display style fraction numerator capital delta I over denominator I end fraction end style close parentheses end fraction space equals space V over I open parentheses 1 plus-or-minus fraction numerator capital delta V over denominator V end fraction close parentheses open parentheses 1 plus-or-minus fraction numerator capital delta I over denominator I end fraction close parentheses to the power of negative 1 end exponent R plus-or-minus capital delta R space equals space V over I open parentheses 1 plus-or-minus fraction numerator capital delta V over denominator V end fraction close parentheses open parentheses 1 space left parenthesis negative space o r space plus right parenthesis fraction numerator capital delta I over denominator I end fraction close parentheses space equals space V over I open parentheses 1 plus-or-minus fraction numerator capital delta V over denominator V end fraction close parentheses open parentheses 1 plus-or-minus fraction numerator capital delta I over denominator I end fraction close parentheses R plus-or-minus capital delta R space equals space V over I open parentheses 1 plus-or-minus fraction numerator capital delta V over denominator V end fraction plus-or-minus fraction numerator capital delta I over denominator I end fraction close parentheses space left parenthesis space n e g l e c t i n g space p r o d u c t space o f space capital delta V space a n d space capital delta I comma space w h i c h space i s space v e r y space v e r y space s m a l l right parenthesis h e n c e space fraction numerator capital delta R over denominator R end fraction space equals space fraction numerator capital delta V over denominator V end fraction plus fraction numerator capital delta I over denominator I end fraction end style
 
in voltage measurement error ±5V in 100V, it means 5% error
in Current measurement error ± 0.2A in 10 A, it means 2% error
hence Resistance measurement has 7% error.
Answered by Expert 6th March 2018, 9:39 AM
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