Question 1

You measure two quantities as A=1.0 ~m 0.2 ~m , B=2.0 ~m 0.2 ~m . We should report correct value for A B as

Accepted Answer

Given, A=1.0 ~m 0.2 ~m , B=2.0 ~m 0.2 ~m Let Y= A B = (1.0)(20) =1.414 ~m Rounding off to two significant digits aligned Y & =1.4 ~m \ Y Y & = 1 2 [ A A + B B ] \ & = 1 2 [ 0.2 1.0 + 0.2 2.0 ] \ & = 0.6 2 20 \ Y & = 0.6 Y 2 20 = 0.6 1.4 2 20 =0.212 aligned Rounding off to one significant digit, Y=0.2 ~m

Question 2

Two resistances are given as R_1=(10 0.5) and R_2=(15 0.5) . The percentage error in the measurement of equivalent resistance when they are connected in parallel is

Accepted Answer

Equivalent resistance in parallel combination is given by aligned & 1 R_ eq = 1 R_1 + 1 R_2 \ & R_ eq = R_1 R_2 R_1+R_2 = 10 15 10+15 =6 aligned Differentiating both sides, we get aligned & R_ eq R _ eq ^2 = R _1 R _1^2 + R _2 R _2^2 \ & R _ eq R _ eq = ( R _1 R _1^2 + R _2 R _2^2 ) R _ eq \ & = ( 0.5 100 + 0.5 225 ) 6= ( 6 0.5 25 ) ( 1 4 + 1 9 )= 13 300 \ & R _ eq R _ eq 100= 13 3 =4.33 \% aligned

Mathematics in Physics — Previous Year Questions & Solutions