The heat generated in a circuit is given by `Q = I^(2) Rt` , where `I` is current , `R` is resistance , and `t` is time . If the percentage errors in measuring `I , R , and t are 2% , 1% , and 1%` , respectively , then the maximum error in measuring heat will be

Options

A. `2%`
B. `4%`
C. `6%`
D. `8%`

Answer

C

Explanation

(3) `Q = I^(2) Rt`
`(Delta Q)/(Q) = 2 (Delta I)/(I) + (Delta R)/(R ) + (Delta t)/(t)`
`(Delta Q)/(Q) xx 100 = 2 (Delta I)/(I) xx 100 + (Delta R)/(R ) xx 100 + (Delta t)/(t) xx 100`
`= 2 xx 2 + 1 + 1 = 6%`